Nonbinary people are absolutely allowed to use different pronouns in different situations.
You might be uncomfortable with your family using they/them pronouns, but be fine with she/her, or vice versa!
You might be fine with some people using gendered pronouns for you, but not others!
You might want people who are strangers or acquaintances to use gendered pronouns, but not close friends or family.
You might want to use neopronouns only when with people you don’t know very well, and switch back to they/them or gendered pronouns when with close friends.
Sometimes your preferences might change!
And that is okay!
This is your life, and you are never putting a burden on someone by asking them to use a specific pronoun with you. You deserve to live the way you want to.