I want to end this relationship!

I recently got into an argument with my girlfriend about something one of her friends said and was surprised because my girlfriend took her friend’s side. I don’t want her to agree with me on everything, but this was such a horrible thing being said that I didn’t expect my girlfriend to not see my point of view. It has changed how I look at her completely because I think I was blind to some of her opinions. I was so madly in love that I simply ignored a part of her personality that is completely different from mine and what I believe in. I don’t think I see a future with her and even though we are great together, I have decided to end this relationship. Am I being too harsh?
You alone can decide what your priorities are and choose to act upon them. If your beliefs are more important than your relationship, you are entitled to pick one over the other. Being harsh or not is not the point here, because you don’t see a future with someone who doesn’t share your point of view. As you point out, you don’t have to agree with each other all the time, but if you think there are some divides that cannot be bridged, the sooner you move on, the better it may be for you both.

Should I try and ask a colleague out without really knowing what her personal life is like? I am pretty sure she’s single because I have chatted with her for almost a year now, but there is no way of knowing for sure. Her Facebook status doesn’t have any clues either. If she is with someone this can become awkward very quickly, so I am hesitant.
The easiest way to avoid any misunderstanding is to be direct. All you’re asking for is a cup of coffee. If she declines, you don’t need to worry about whether she is single or not. If she accepts, you can ask if she’s single.