Using Old Testament passages against remarrying one’s spouse seems problematic in light of Christ’s later teaching.
Not really. Just because Jesus spoke about the Ten Commandments doesn’t mean that we don’t need to learn them, after all. And even if we don’t sacrifice animals in the Temple any more, it’s still worth studying because it gives us deeper understanding of what it means and the character of God.
Anyways.
Jesus said that divorce happens because of the hardness of our hearts.
And our hearts are still hard.
Jesus never said that there’s no such thing as divorce, just that God never meant intended it to happen, and that God hates it. But divorce DOES happen; you just need to look around to see that.
So it’s not any kind of stretch to look at God’s Law involving the behavior of a divorced couple in order to determine what to do when divorce does happen.
And God says that remarriage—except maybe in the case of adultery, but again that’s not relevant to the point at the moment—is sin. But also that re-re-marriage, even to your original partner, is ALSO sin.
But like all sin, divorce and remarriage is covered by the blood of Christ. Confess it; absolve it; don’t do it again. And you’re still part of the Body of Christ.