Today, I am reading and commenting on Ezra 9-10.
The problem with mixed marriages was not that the women many of the Returned Exiles had married were not of Jewish decent. The problem was that they did not worship God. Many of the Returned Exiles had married women who continued to follow pagan religious practices, and these men joined their wives in those practices. There was no easy answer to this problem. The decision was made that those who were married to women who continued to follow pagan religious practices needed to divorce them. However, it was acknowledged that this needed to be addressed on a case by case basis. The fact that they decided to address the issue on a case by case basis tells us that it was not simply a matter that every man who had married a woman of non-Jewish decent needed to divorce her. Clearly, those whose wives had fully adopted Jewish religious practices were allowed to keep those wives.