I'm not Christian (or religious) but I believe I have high moral standards, many of which are aligned with the teaching of the church. I don't think being a good person and being Christian (or any other religion!) are mutually exclusive.
Honestly, your girlfriend's reasoning behind not wanting to marry you sounds like an excuse to me... If she didn't care before, it makes no sense that she cares so much now!
I actually find a lot of Christians far less moral in their behaviour than many non-Christians, so to me, being Christian or religious or not means very little about the core of a person!