"I'm really sorry but it makes me uncomfortable, I dont want to get into it." You could also say how it's like how you don't want to put other personal information.
Nope. Nope. NOPE.
as other pp have mentioned, i've spent around 40 years mostly in male dominated industries fighting a bloody hard fight, and making only incremental progress compared to less good men, to throw it all away now with a "she/her" at the bottom of my email.
One of the ways i do this is "think, how would a man write this?" on all correspondence. And the word "sorry" is always the first to go. I delete unnecessary greetings and "please" and "sorry" and "thank you" are the first to go. I absolutely refuse to take notes during meetings, i don't make tea or coffee, i barely ever mention my children and i don't bring in cakes unless it's my birthday. I sign off either "firstname lastname" or "initial lastname" and i have never ever made a comment if i get correspondence addressed to "mr".
Up to now i haven't been asked to add my pronouns, but there is no way i will. And i will just say "no, i won't be doing that" with no explanation and no apology. I am perfectly happy for others to do that, and am entirely happy to use whatever pronouns they want. But i won't be joining in.
I have worked with a lot of Asian companies over the years and it is mostly not clear, when they're not using western names, if they are male or female. I tend not to address them as "mr" unless i know for sure, and try to use gender neutral language until i do know. But that's just my preference.