None of the Old Testament prohibitions against incest are repeated in the New Testament.
This is true. The specific incest laws from the Law of Moses are not repeated in the New Testament.
But, Paul condemns the man in 1 Cor 5 who is sleeping with his father's wife. He says that even the Godless Gentiles do not do such evil. The Christ followers of Corinth were proud, boasting that they were so tolerant that they accepted such a sinner. But Paul condemned him and cast him out of the assembly of saints so that he might repent and be saved.
He was not condemned for incest. No, he was condemned for sleeping with a married woman: his father's wife.
Neither slavery nor polygamy are condemned anywhere in the Bible.
Not so fast here. Slavery is not condemned, but polygamy is.
Mark 10:6-9 makes it very clear that from the beginning, from Creation, God intended for marriage, sexual relationships, and intimacy to be between one man and one woman for life. After the death of one spouse, the other is free to remarry. But as long as both live there is supposed to be only those two together. Because of man's sinful nature, God allowed man to divorce, but that is not what God intended.
In fact, various commandments and instructions in both testaments regulate their practice. For example, in the New Testament a polygamist cannot be an elder.
So only one man with one woman, thus the elders are supposed to be the examples for the congregation of the Church they lead. They are not to be living in the sin of polygamy, nor any other sinful lifestyle, and still lead the congregation over which they are shepherds.
That implies that there were polygamists in the New Testament church and that they were not prohibited from practicing polygamy.
That implication does not condone the sin. It simply points it out, and forbids the office of overseer to those who practice that sin.
The only instance where divorce is commanded is in the books of Ezra and Nehemiah where the Israelites were forced to divorce their non-Jewish spouses. That was clearly based on the Law given to Moses.
These marriages were not sanctioned by God, because they were a violation of an already established Law. The men were told to divorce their wives to bring themselves back into line with the Law of Moses. This was not really "divorce", but was ceasing to live in an unmarried (unsanctioned marriage) sexual relationship with these women.
Even in the New Testament Christians are not commanded to divorce their non-Christian spouses, although mixed marriages are strongly discouraged.
Correct, we are not told to divorce our non-Christian wives, but to live with them peacefully as long as they are willing to live with us, because in so doing we may bring them to salvation.