I'm not going to acknowledge my cousin's pronoun preference for my child
Why are you against it?
I think it's ridiculous. People are either male or female.
It's okay to have your opinion. You should be respectful of what others want, though. If someone has a personal pronoun preference, it doesn't hurt you to use it.
It's not hurting me. You should learn new things.
I think that you might try to listen to her better. I think that it is important to acknowledge pronouns these days.