Is it wrong to date my sister's friend who's also my friend?

There's a girl I like currently who's in my grade, but she's also close friends with my younger sister. I've known this girl for about 4 years now, all throughout High School, and I didn't really start having feelings, and I mean strong feelings for her until August of this year. We've got differing political opinions (she's liberal, I'm conservative), but surprisingly we do have similar interests. I enjoy the arts, she loves them. On top of that I also love to sing, and so does she.

Moving on though, my sister claimed when I brought it up that I liked her that it was "gross" and she didn't want me mingling with her friends. I really can't understand my sister's logic, especially considering that this could benefit her more than it could hurt her. It's ironic because people usually associate her with being a good person, but it's really moreso me who is that way. Now my sister's preventing me from being able to even ask this girl on a date, and I really like this girl.

I have plans to try and get a commission in the army when I get out of high school, and I REALLY want to try and make this work. I really do like her, but I don't know what to do now that my sister has said what she's said.