For him, as a black man, the LDS faith had some history that was directed at his ethnicity and so he wasn't comfortable joining. To him that was a higher priority than sharing a religion (which may not have been a huge deal to him at all).

Islam, of course, has its own checkered history, but those issues generally aren't directed at black men, so (from his perspective) that wouldn't be as much of a dealbreaker.

Now, from her perspective/background, Islam's past could certainly be more of an issue, but honestly it looks like the driver for all this (for her) was mostly just wanting a common religion, whatever it was.

If that's her #1 priority (more than any doctrine or historical injustices) and he's unwilling to join hers (for whatever reason), then the only way to accomplish her goal is to join his.