Well no, he has the exact same rights as any other citizen to vote and donate for whatever laws he prefers.

It's inappropriate to do various things that hurt people around you; but it's perfectly fine to vote and support laws that directly affect quality of life of people in both directions (surprise - pretty much all laws/propositions do!).

It's exactly the same as boycotting a company because CEO belongs to a really opposite political party - USA doesn't have any really opposite parties; but the rest of the world has seen quite a lot of such partisanism, and it ends up just as ugly as any other bigotry.

I think you missed the part where one husband in this couple was granted a green card due to marital status, and was able to immigrate to the US.

So there would be no or little recourse, much less voting.