I think the best response that’s always worked for me is:

“Who cares!” Person riled up about this inclined to agree with me because they think I’m on the two genders “side of the debate”. “Just try your best to call people what they want to be called and move on. If someone’s name is x, try call them x, if they say ‘I am a y’, try calling them a y. If you get it wrong accidentally, oh well, just say sorry and try again. Why are we even still talking about this? It’s such a non-issue”

Highly effective on those who aren’t super conservative and just been swept up in the (in my opinion) astroturfed outrage.