I was talking with a preacher back in the 1980's from an anti Church of Christ and he explained a verse in the Old Testament proved God allowed re-marriage for causes other than adultery. I asked for the passage but he didn't want to share it with me because he was still studying it to make sure. He never got back with me. Since the church has begun to lean in his direction. He never told me where he got it from but over time I figured out their position and many still teach their error. It is an error.
In their exegesis they make several mistakes and I will go thru a few. Probably the easiest to see is that Jesus never used or endorsed their idea. Jesus simply says re-marriage except in cases of fornication was adultery. So, even though a case can be made from the Old Testament and even a couple New Testament passages, Jesus never used or endorsed their theories. Jesus simply said re-marriage is adultery. Jesus acknowledges the second marriage is accepted in our secular laws but still calls it adultery.
The first mistake is marriage under our govt laws may be legally valid, but not endorsed by God. You can legally get married and divorced 10 times, but God still calls it adultery. The wording of Jesus is very clear. He doesn't say the new marriage is legally invalid, he simply shows a legal marriage can be adultery.
Matthew 19:9
And I say unto you, Whosoever shall put away his wife, except [it be] for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery.
A second mistake is in assuming the Law of Moses was perfect as a law of God. It was perfect for its purpose but not perfect in every regard. The New Testament law of Christ is superior. So, assuming what Moses commanded is God's final judgment is short sighted. Moses allowed re-marriage because of their hard hearts. It was temporary perhaps to protect women. That is a theory. We still know it was temporary and imperfect. Compare these verses.
2 Corinthians 3:7
But if the ministration of death, written [and] engraven in stones, was glorious, so that the children of Israel could not stedfastly behold the face of Moses for the glory of his countenance; which [glory] was to be done away:
2 Corinthians 3:9
For if the ministration of condemnation [be] glory, much more doth the ministration of righteousness exceed in glory.
1 Corinthians 13:10
But when that which is perfect is come, then that which is in part shall be done away.
We should understand the law of Moses was temporary and imperfect.
Galatians 3:19
Wherefore then [serveth] the law? It was added because of transgressions, till the seed should come to whom the promise was made; [and it was] ordained by angels in the hand of a mediator.
The law was simply a stop measure to address some transgressions, such as mis-treatment of a wife,