If your girlfriend didn't tell her father about you or seemed to miss a few details out for him to be surprised, your race for example, maybe she expected a slight reaction from him? Though that might make her sound terrible, which i'm not trying to do, it's a possibility. Your girlfriend should have explained to her father she was in a relationship with you, told him a bit about you and for lack of a better word "prepare" him for meeting her brand new boyfriend.
I'm not sure how old you two are, she should be able to make her own decisions. Her dad isn't the one dating you but in my opinion, and this opinion has got me into trouble many of times, it's actually none of his business. He has every right to want whats best for his daughter but who says that you aren't whats best for her? Him? Well, he doesn't know you. Every parent deserves respect but for them to be respected, they must learn to respect you in return. He doesn't do this.
If you two really like each other then I don't see why you shouldn't be together. You just need to support each other through it because it will be difficult. Just talk to her, see what she thinks and what she wants and you two will figure it out. She needs to sit her father down and talk to him, it will be a nightmare to do but sometimes these things need to be done.