I'm going to break up with my boyfriend because his brother is a white supremacist
This is a very serious accusation. What makes you think his brother is a white supremacist?
I saw the posts on his facebook.
Not wanting to be associated with people who tolerate hate speech is understandable. However its unrealistic that family members can control what other family members say on social media. Try talking to your boyfriend and see how he feels about it before breaking up with him.
I am going to break up with my boyfriend because I don't want to be with a family member who tries to hurt minorities.
I appreciate your concern but your boyfriend is not his family. It is bad to punish people for things their family may do.