Edit: I’ve since been persuaded that being able to play around with pronouns is actually really valuable to trans people, particularly those who aren’t out. I retract this post.
Sometimes I’m at a gathering of people where, during introductions, someone suggests that we introduce ourselves with our names and our preferred pronouns. Most people introduce themselves with what you would expect (“I’m Julia and I prefer she/her”), and one person, usually the person who asked for the exercise to be added, has something more novel (“I’m Alex and I go by the gender-neutral pronouns ze/zim.”)
I’m still not sure how I feel about this protocol. The idea is that it places equal emphasis on everyone’s pronoun choice rather than one person having to introduce themselves with something special, but I think the effect is that everybody spends the exercise thinking, “Okay, who’s the outlier?” In theory transgender allies could suggest that every introduction everywhere include preferred pronouns, but I’ve never had the guts to do it. There are so many other pieces of data one might want to share during an introduction (“I’m Andrew and I have a cold, so I won’t be sitting too close to anyone”) that I don’t think it makes sense to make everyone repeat them all.
At such introduction sessions, there are always a few people who say, “I’m Rachel and I don’t care what pronouns you use with me – anything’s fine” Which is fine if he really has no preference about what pronouns other people call zer. Likewise the person who suggests “My preferred pronoun is zippy!” I doubt that this is what zippy actually prefers people use with zippy in daily life.
I’m sure there are people who genuinely don’t care. But my sense is that most of us have never experienced being consistently called by a non-preferred pronoun, and we would find it deeply weird if this started happening. It’s easy for me to not think about what it would be like if everyone started calling me “he” or “ze” or “zippy”, because it’s never happened to me. But my guess is that it would bother me. This is one of those cases where the joke is novel to the maker but not to the listener.
So answering with “I don’t care what pronouns you call me” or suggesting a joke pronoun is okay if you have really considered this and genuinely would be prefer it. But to me, it comes off as making light of how yucky it is for people to be called by pronouns they hate. Which is easier to do if you’ve never been in their shoes.