Girlfriend refuses to go out in public until i shave beard; says i look like rapist?

Why does it matter? Is she not your gf because she likes you the way you are, or is she trying to change you? Dude its all starts with changing one thing... imagine if you end up marrying her? I think you should do the same to her and make her see how her making you shave your beard makes you irritated. Say I'm not going out with you in public unless you get a haircut or take off the makeup... I don't know... just don't say it in a mean way because then she will try to make a fight off of it to make up as an excuse for changing the topic. Well hope that helped.