Do you think it is wrong for me to refuse to be friends with someone because they have acne?
So you are planning on not being friends with them just because they have blemishes?
I can't stand to see somebody who looks that way.
It is horrible to not be friends with someone just due to acne. It is not their fault that they are growing up and getting acne. If you do not like them for their personality then that is one thing, but to refuse them due to how they look is pretty low.
I have an irrational fear of acne and their face makes me feel weird. I just can't be friends with them.
It's wrong and shallow to deny a friendship because of acne. You should consider how you would feel if someone did not want to be friends with you because of a physical flaw that you have.