So I think this is an interesting question, worthy of reflection. Now, my own answer to this is a conditional yes, but only on matters which relate to Biblical theology.
Now, before I begin with a discussion of acceptable cases, based on current events and historical precedents, I think it is important to establish why, ordinarily, the church should be apolitical, and why partisan / party-political intrigues, sex scandals such as the infamous Monica Lewinsky incident or crude and inappropriate remarks by more recent figures, should be beneath the Church and not subject to official mention: the Church is principally a Hospital of Souls; we are concerned with the Realm of God and not the Realm of Caesar, and we exist to provide for the cure of souls, administering the sacraments for the dispensation of the life-giving grace of the Holy Spirit and edifying the faithful through homiletics, hymnody, and the recitation of sacred scripture. As such, any action which might alienate hearers, catechumens, and those weak in the faith, or cause divisions or schisms, or scandalize the more pious and devout in the clergy, choir and congregation, should be avoided, as we should recall the counsel of St. Clement in his epistle, that schism is worse than heresy.
I think the ideal balance can be found in one of the three great televangelists, Archbishop Fulton Sheen, memory eternal, who did discuss social issues, but in an apolitical world. As Christians, we have a vocation to oppose evil. So, for example, the Church is right to oppose genocides, abortions, euthanasia, cruelty to animals, such as dog-fighting, and the wanton and unjustifiable implementation of capital punishment, specifically on elderly inmates who have been imprisoned for years and no longer pose a threat to other inmates, or the excessive cruelty we see in Japan with regards to the dating of executions, and the apparent procuratorial bias in Japanese courts. And of course, the genocides and dispersal of Christians and other minority religions in the Middle East, Pakistan, and Burma, including Yazidis, Mandaeans, Bahais, Falashas, Alawis, Alevis, Bektasis, Mevlevis, and also at-risk groups including Yarsanis, Samaritans, Karaite Jews and the Beta Israel, not to mention all Christians in the Middle East, Pakistan, India, Bangladesh, Indonesia, China, North Korea, Mongolia, Central Asia, and Africa.
And to a greater extent, the extremely large number of executions in Singapore, the Republic of China (Taiwan) and especially the People’s Republic of China, for offenses other than murder, for example, drug trafficking in Singapore and the ROC and corruption in the PRC. And even more so, we should oppose the brutal executions that are commonplace in Saudi Arabia, Iran, Pakistan and other Islamist dictatorships, especially the execution of converts to Christianity, while at the same time following the Orthodox custom of immediately glorifying martyrs as saints; for example, when the 18 Copts and the Ghanaian national who stood in solidarity with them, saying, “Their God is my God” were beheaded by ISIS, the Coptic Orthodox Church instantly declared them saints and an icon was produced within weeks. And when a similar mass beheading of Ethiopian Orthodox Christians occurred, the Ethiopian Church responded with the same haste. This is because the definition of a saint post mortem is someone who is in Heaven and will be judged among the righteous before the dread judgement seat of Christ Pantocrator, and martyrs (those killed for refusing to renounce Christ or on account of their Christianity) and confessors (those who suffer tortures or gross hardships for either practicing Christianity or refusal to recant their Christian faith) have the Gospel promise of our Lord, “He who confesses me before men, I will confess before the Father.”
This should also inspire us to be extremely open about our Christianity; we should follow the example of Saint Anthony the Great, who dared the Romans to martyr him, unsuccessfully; when this failed he followed what the Eastern Orthodox call the “white martyrdom” of holy asceticism, being the first well known hermit (although his definitive biography, The Life of Anthony, by St. Athanasius the Great, which I think all Christians should read, along with On the Incarnation, for Athanasius was instrumental in preserving the faith at Nicaea, and gave us our New Testament canon, recounts St. Anthony’s encounter with another hermit, who survived at an oasis by the will of God, the mysterious figure of St. Paul the Hermit). There is also the “Green martyrdom” of Holy Matrimony, which is self-sacrifice for the good of one’s spouse and one’s offspring (green in Eastern Orthodoxy symbolizes the Holy Trinity and also new life; it is the liturgical color on Palm Sunday, Pentecost, and usually, interspersed with gold, on the Feast of All Saints, the first Sunday after Pentecost (when the Western Church celebrates Trinity Sunday; in the Byzantine Rite this might be superfluous insofar as Pentecost is among other things a feast of the Holy Trinity).
Among those who suffered the Red Martyrdom, however, St. Dietrich Bonhoeffer, who I venerate, I think represents another ideal example of correct Christian political involvement. He, and the other pastors of the Confessing Church, dared to call out both the Nazis and the hypocrites who were their counterparts in the arguably heretical Reichskirche). These were essential matters of Christian virtue.
Another example of valid political intervention is that of St. John Chrysostom, who sharply criticized Emperor Theodosius II, his wife, and the Imperial court in Constantinople for their decadence during a period which an analysis of Roman history shows to be one of great hardship, as the Western Empire began to crumble, and no doubt this resulted in severe suffering in Rome, and impoverished migrants into the Eastern Empire in border regions, like Dacia and Thracia, which fell to invading tribes, as well as Libya, and the ports of Brundisium, Messina and Ravenna. The last straw for Theodosius II was when St. Chrysostom disclosed while preaching at the Hagia Sophia that the Empress had purchased a solid gold toilet, and lamented this money had not gone to the poor. For this he was exiled in 404, and after an unsuccessful attempt by his colleague the Archbishop of Rome, and two other Archbishops, to have him restored as Patriarch of Constantinople, he was deemed a danger and was exiled again to a more remote place in 407, but died en route, which suggests he may have been death-marched. Liberals should remember however that this was a criticism of the ruling class, who had not only wealth but political power, and were living a life of absurd and pointless luxury, during a time of extreme hardship; the example of St. Chrysostom is not a license to preach socialism or liberation theology, but rather is an example of “speaking truth to power”, exposing kleptocratic corruption that was arguably endangering the survival of the Western Empire and the long-term viability of the Eastern Empire and causing death from starvation among those left destitute by the crumbling provinces, infrastructure and civil institutions of Old Rome, which would be sacked within the course of the fifth century, and the Western Empire would collapse, bringing about the Dark Ages in Western Europe.
Finally, there is one more example of correct political involvement, and that is St. Mark of Ephesus, the only bishop of the entire Holy Synod of the Church of Constantinople to object to the Council of Florence, in the late 1430s, in which, encouraged by the Emperor, the Ecumenical Patriarch of Constantinople and all of his bishops except St. Mark agreed to recognize and submit to the supreme ecclesiastical authority of the Roman pontiff, in return for military assistance against the rapidly advancing Ottoman Empire. St. Mark appealed to the laity, who courageously chose the Kingdom of God over maintaining terrestrial power, and submitted willingly to 370-420 years of Turkocratia, which ended gradually after the Greek revolution, and later in the 19th century, the intervention of the European powers following genocidal atrocities committed against the Bulgarian people by the Bashi Bazouks, bloodthirsty mercenaries used as terror troops by the Sublime Porte, against Ottoman provinces and tributaries that failed to toe the line and comply with the demands made in the name of the Sultan (who was also Caliph).
So this provides us with another form of sociopolitical issue, closely related to the case of St. Dietrich Bonhoeffer; in the former case, the Confessing Church opposed both the policies of the Nazi State and the Reichskirche in supporting them, whereas in the latter case, St. Mark and the laity of what remained of the Byzantine Empire in the 1430s after its prior conquest and despoilation by Venice in the Fourth Crusade, and 700 years of war with Islamic caliphates, decided to accept the consequences of refusing Western military aid, including total defeat and subjugation, which at the time seemed probable, and proved inevitable, to compromising the principles of the Christian faith as they had received it.
This being said, the Church should never involve itself in partisan politics. Another of the three great televangelists*, Dr. James Kennedy, memory eternal, who I greatly admire, did on occasion go beyond the pale when it came to political advocacy from the right, and the United Church of Christ alienated me by among other things engaging in excessive political agitation, which has been a Congregationalist vice since the Revolutionary War, when the British labelled us the “Black Robed Regiment” for our vocal support of the Revolutionary Cause, from the pulpit. In agitating so ferociously, I fear we failed loyalists and unionists, alienating them and causing them in some cases to join churches which might have substantial doctrinal differences, for instance, the Baptists. But, this was in a prelude to the Congregational-Unitarian schism, and I would argue that that schism resulted in the most stridently political parts of the Congregational Church in America becoming Unitarians, and later, Unitarian Universalists (though the unfortunate merger of the Unitarian Church with the Universalist Church, which has had the undesirable effect of leaving Christians of a Universalist persuasion without a denomination of their own). Liberation theology also has a tendency to be excessively political. The church should not care about arguable points of political opinion, such as monarchism vs. republicanism, the correct ratio of socialism vs. capitalism; Keynesiasm vs. Monetarism, the correct approach to infrastructure development, or worse, party politics.
In all cases however, extreme discretion should be used when it comes to the correct forum for ministers to preach on these rare cases where the Christian conscience compels the Church to act. The Eucharist is seldom an appropriate venue, for it is chiefly an act of worship to God and a means of grace for the participants. Even on an issue as important as abortion, the only liturgical commemoration I can think of where a Eucharistic homily could touch on this issue is the Feast of the Holy Innocents, which like most feasts in Christmastide, suffers from a scandalous lack of attendance, and also, on those occasions where Matthew 2:13-27 is read, which in the Revised Common Lectionary, occurs only on the First Sunday after Christmas in Year A, which means, it is head only once every three years (or four years in those churches which have taken the bold step of improving the RCL by introducing Year D, which I highly recommend), on one of the least-attended liturgical days in the church year.
So, I propose the Divine Office is a better place to preach about these pressing issues. St. Chrysostom famously preached most of his great sermons in the Ninth Hour, and I am strongly in favor of reviving the Ninth Hour in all churches as a commemoration of our Lord and Savior Jesus Christ, God incarnate, dying on the cross in order to recreate humanity in His image, saving us through His sacrifice, and enabling our resurrection after His example. As a penitential prequel to Sunday Vespers or Choral Evensong, the Ninth Hour is also an ideal time to preach the essential moral values of Christianity. Preaching in the Eucharist should be limited to homiletics which in lectionaries where the texts are interconnected, like the Western Rites, might provide a three-point exposition of the texts, whereas in lectionaries where they usually are not, such as the Byzantine Rite except on holy days, might provide an exposition of the liturgical theme of the day, or an exposition of one of the texts, or if there is a providential relationship between the Gospel and Epistle (which tend to be asynchronous due to something called the Lukan Jump, where Matthew, which has been read lectio continua since the Apostles Fast, is replaced by Luke, whereas the epistles continue to be read lectio continua until Septuagesima). Another option would be to use Morning Prayer before or after the Eucharistic liturgy for preaching. Churches with two or more presbyters might do well to have one do the bulk of the work in the Eucharist, and the other preach, resting as much as is possible in a sedilla if they are available in that tradition.
Only in the most extreme and urgent cases should a secular issue challenging our Christian morality be addressed in the Eucharistic liturgy itself, and ideally, in such emergent situations, the time to do it would be when the most people are present, typically the start of the service in Western churches and the end of the service in Eastern churches, ideally outside the beginning and conclusion of the actual liturgical service itself, in the form of a supplementary announcement or address. For example, one could start by saying “Dearly beloved brethren, before we begin the Holy Communion service, there is an urgent matter we must consider,” or “Before we leave, or eat lunch together in the church hall, I am compelled to bring to your attention a most urgent matter...” Although one might do well to avoid my archaic turn of phrase in most congregations.
So, in conclusion, we should follow the example of St. Dietrich Bonhoeffer, St. Mark of Ephesus, and St. John Chrysostom, but avoid the extremes of liberation theology, assorted right wing megachurches, the United Church of Christ, and partisan politics in general, lest we alienate people over trivial matters, and cause them to become unchurched, for in such cases by offending them we have effectively disfellowshipped them, and cut them off, without justification, over secular issues that are of no concern to God. The intervention in political matters is an extraordinary measure, for extraordinary circumstances; an emergency response to emergencies, and the intensity of the intervention must be proportionate to the severity of the situation. This is the case in selecting the proper forum within the services of the church to discuss this matter (Dr. Kennedy properly reserved his most political content for the program he broadcast after the conclusion of the worship service at Coral Ridge, and as mentioned before, the moral sermons of St. Chrysostom were preached in the ninth hour).
*The three great televangelists in my opinion are Archbishop Fulton Sheen, Rev. Robert Schuller of the Crystal Cathedral, and Dr. James Kennedy of thenCoral Ridge Presbyterian Church. And the greatest evangelist of the 20th century, whose work in the Soviet Union was an invaluable service to the Russian Orthodox Church, was Rev. Billy Graham.