Ok,
Like a few of the other posters I'm Christian and my girlfriend is not. I do not share the same beliefs as her (or most of my friends for that matter) on a few issues, and the same probably applies for about everyone else I'll meet for the rest of my life.
Now firstly I'd like to clarify that I was never as Fundementalist Christian as her but I still believed in Creationism etc. and thought that God was a puppet master and we all marionettes in his big "plan".
Up until the age of about 10 I had never met anyone who wasn't also Christian. When I did I argued with him. For a long time. Eventually I realised that I was being foolish and we became firends. Once I got to highschool I went from spending about 5% of my time with non-Christians to spending about that much time with Christians, and I can honestly say that my beliefs have been changed by that alot, and in a good way.
Now let's say that you end up in a relationship and everything is fine and dandy and she ends up spending about half of her time with non-Christians who she meets through you. She will almost definately, at one point in time talk about her beleifs with them. Eventually she'll come to accept that people don't all share her beliefs and I'm sure she'll deal with it. On the topic of the "Obama hating, bible bashing etc"; do you honestly think that she will stick to her guns about things like homophobia or racism? In this day and age?
You will never meet someone who is "perfect", you may meet someone who is close. She mightn't be the closest you'll find to your idea of perfect but it's just as likely that she is.
Worst case senario: You go out with her. You're happy for a few weeks. She nags you and you're no longer happy with the relationship. You have a massive fight and break up and don't talk to her ever again. How are you in any worse a place than you were before you met her?
or
Worst case senario: You don't go out with her. Save a lot of time, money, heartache etc. You regret it for the rest of your life.
In the end all that you ever need to worry about in a relationship is whether or not you're happier as a cause of the relationship. That goes for friendships too. If you genuinely think that she'll cause you more greif than happieness then don't have a relationship with her. Honestly though, I can almost guarantee that for at least a little while she'll make you happy, even if it's only as a friend.
It all comes down to that. In fact, I would argue that in all facets of your life, as long as no one if being harmed by your actions, you should always be doing things that will either make you happy or bring you closer to happiness.
The ball is in your park.