How do you handle identity rejection??

So, I am 24 years old and have been bi for as long as I can remember. my mom is supportive, but my dad and stepmom are in denial. I am gender fluid and was told it was a phase. I go by chase most of the time. they were informed but everyone in my life, but a handful of people refuse to call me that. my younger sibling goes by a different name and some of my friends support another friend with their name change but not me who has been in the friend group longest. so, my question here is how do you handle the rejection? I know who i am and have expressed to them who i am so why does it still bother me so badly? I just have let it go and go by chase with those who accept me but my birthname by those who don't. do any of you ever experience this?