I'm going to be friends with my best friend's ex
Is this something that you are doing on purpose?
I consider her to be an awesome girl.
While your best friend may not be happy that you are making friends with their ex, it is also not fair for them to keep you from who you want to become friends with. This matters more on the context of their relationship. If the breakup was very difficult, you may want to avoid your best friend's ex to avoid upsetting your buddy.
I don't care.
I was saying some people might have a real problem with this. It looks really weird and might make it seem like you want to date your friends ex if you get close and you wern't before.