JGG asked:
Is divorce and remarriage still a sin?
Yes. A husband is never to divorce his wife for any reason (1 Corinthians 7:11b), just as a wife is never to divorce her husband for any reason (1 Corinthians 7:10). But if a wife does divorce her husband (such as to escape domestic violence), she must remain unmarried or be reconciled to her husband (1 Corinthians 7:11). A Christian must always completely forgive everyone who has wronged him or her in any way (Mark 11:25), no matter how great the wrong and no matter how many times a wrong has been committed (Matthew 18:21-35). For if a Christian refuses to forgive anyone for anything, God will refuse to forgive that Christian for his or her own sins (Mark 11:26).
The fornication exception in Matthew 19:9 permits a husband to divorce his wife for fornication and marry another woman without his committing adultery. This may apply only to cases where a husband discovers that his newlywed wife isn't a virgin (cf. Deuteronomy 22:14, Matthew 1:19). There's no such fornication exception granted to a wife. If a wife divorces her husband for any reason and marries another man she is committing adultery (Mark 10:12). Also, there's no fornication exception granted to a man who marries a divorced woman. If a man marries a woman divorced for any reason he is committing adultery (Luke 16:18b).
God never said that marriage would be easy, and he has set such strict New Covenant (New Testament) rules regarding divorce and remarriage (Matthew 19:9) that the apostles said that it's better not to get married at all (Matthew 19:10). Jesus answered them by saying that whoever can accept not getting married and remaining celibate should accept it (Matthew 19:11-12). Paul the apostle said the same thing, that unmarried celibacy is the best thing for a Christian if he or she can handle it (1 Corinthians 7:1,7,8,32-35). But if someone who hasn't been married can't contain himself or herself sexually, he or she should get married in order to avoid fornication (1 Corinthians 7:2,9), in the sense of unmarried sex.
The only unpardonable sin is blaspheming the Holy Spirit, such as by ascribing a work of the Holy Spirit to the devil (Mark 3:22-30). Any other sin can be forgiven if it isn't continued in and is confessed to God (1 John 1:9). Just as if Christians find themselves living in the sin of an adulterous affair, so if they find themselves living in the sin of second-marriage adultery (Mark 10:12, Matthew 19:9), they can't continue in that sin (or any other sin) and expect God's grace to forgive them (Hebrews 10:26-29, Galatians 5:19-21, 1 Corinthians 6:9-11). They must break off with the second spouse, even if they've had children with the second spouse, just as married people must break off an adulterous affair, even if they've had children as a result of that affair.
After breaking off an adulterous second marriage, a wife doesn't have to go back to her first husband: she can remain unmarried if she can't be reconciled to her first husband (1 Corinthians 7:11). But she can't marry someone else, even if, for example, marrying someone else would help her and her children to escape poverty. For just as escaping poverty wouldn't justify the wife continuing in the sin of an adulterous affair with a man who financially supports her and her children (or wouldn't justify the sin of her becoming and remaining a well-paid prostitute), so escaping poverty wouldn't justify the sin of her entering into another case of second-marriage adultery with a man who financially supports her and her children.
Jesus' New Covenant (New Testament) teaching that divorce and remarriage is adultery abrogated the Old Mosaic Covenant teaching which allowed divorce and remarriage (Matthew 19:7-9, Matthew 5:31-32). Jesus' New Covenant (New Testament) commandments far exceed in righteousness the Old Mosaic Covenant commandments (Matthew 5:20-48), which have been abolished (Ephesians 2:15, Hebrews 7:18-19, Colossians 2:14).
Matthew 5:17-18 is referring to Jesus coming the first time to fulfill all of the Old Testament prophecies regarding the Messiah's first coming (Luke 24:44-46). Jesus taught that Christians have to obey his New Covenant (New Testament) commandments, such as those he gave in the Sermon on the Mount (Matthew 5:19-7:29) and in the writings of Paul the apostle (1 Corinthians 14:37, 1 Thessalonians 4:2).
Romans 3:31 means that Christians establish the Mosaic law not in its letter, but in its spirit (Romans 7:6), by loving others (Romans 13:8-10, Galatians 5:14). Part of loving others is warning them if they are living in sin (Revelation 3:19, 1 Corinthians 5:1-13 & 2 Corinthians 2:6-8, 2 Thessalonians 3:15, Hebrews 3:13, James 5:19-20). The worst thing a Christian can do is to coddle people who are living in sin, instead of sharing with them the hard truths of God's word (2 Timothy 4:2-4, cf. Jeremiah 23:14,22,29). Telling the truth to people can sometimes hurt them, but it's better than deceiving them with something that makes them feel good (Proverbs 27:6, Proverbs 28:23). The reason that second-marriage adultery (or any other sin) is so common in the church today is because so much of the church has stopped preaching and believing the hard truths of God's word (2 Timothy 4:2-4, cf. Jeremiah 23:14,22,29).
Regarding 1 Corinthians 7:15, it simply means that a believing spouse shouldn't fight an unbelieving spouse if the unbelieving spouse is dead set on divorcing the believing spouse. 1 Corinthians 7:15 doesn't mean that the believing spouse, after being divorced, can then marry someone else.