is it wrong to not talk to my cousin because she's a lesbian?

Yes it’s bigotry and against bible

Nope. Nothing terribly wrong with that.

the day you need blood youll regret it

No, I think you'd be doing her a favour. It's obvious that your a bigot. You obviously never cared about her or you wouldn't care that shes a lesbian. No one needs a bigot or a racist in their life.

Yeah it is. If that’s the only reason you can find, then that’s wrong. She can’t control who she likes. Having a supportive cousin could make a whole lot of difference to her. Her sexuality shouldn’t change your relationship. 

Yes, of course it is.

Yes.  Assuming your doubtful story is true, if you refuse to talk to someone for the sole fact of that person's sexual orientation, that makes you a bigoted asshole.

Why do you want to be a jerk? There is nothing wrong with your cousin. You are just being a jerk!!

Yes it is wrong, she was always lesbian!

Yes, of course it is.

What is she doing to upset you?

She's not doing anything wrong or evil or harmful.

She just happens to be only attracted to other females.  How does that concern you?