My girlfriends sisters hate me!?

Ok I've been dating my girlfriend for a year. (We're both in our early 20's) Her sisters though just can't stand me. Especially her little sister who is 19. I have been nothing but nice to her since I've met her. Inviting her out whenever we go out, showing interest in her dancing, even asking my girlfriend if we should invite her because she seemed lonely that day. I have done nothing to make her think I'm anything other than a great guy. Recently she refused to go somewhere with me and my girlfriend because I was attending and only was willing to go if another person came to keep her company. It's very insulting. This however is not the main issue. My main problem is that my girlfriend seems to be completely ok with it. I have asked her to stick up for me and while she says she has I'm not sure. She thinks I should just ignore her little sister but it's when her twin sister hates me when I have to go. This right here is the problem. Their not identical twins and neither of them believe in that bogus twins are telepathic crap but they are very close. So according to her if her twin does not approve of me she won't. What crap is this? If I'm dating someone I don't care if my entire family hates them I will still date them if I want to but if her sister doesn't like me I have to go? I am really questioning this past year and don't want to be involved with someone so impressionable. Should I dump her and her stupid sisters or should I forget what they think and bear it for my otherwise great girlfriend?