There are people who vote Republican in private, and they are different from those who loudly proclaim their Republicanism to everyone they encounter. It might be a shame that the private Republicans vote how they do, but that doesn't have to affect their ability to engage with trans people, or vice versa.
So I would say the problem is not the ideological divide per se, but the 'identity' politics which makes both sides openly intolerable to each other. Of course, it's problematic because trans people can't keep private in their transness at a game of cards in the way that a radical socialist could. But in modern discourse, we're all encouraged to be loud and proud in order to advance our preferred politics, instead of quiet and demure in order to foster community that transcends politics.
So I would say the problem is not the ideological divide per se, but the 'identity' politics which makes both sides openly intolerable to each other. Of course, it's problematic because trans people can't keep private in their transness at a game of cards in the way that a radical socialist could. But in modern discourse, we're all encouraged to be loud and proud in order to advance our preferred politics, instead of quiet and demure in order to foster community that transcends politics.