Wars have been fought over a difference of religion...
And people in this age and time actually still believe a difference of religion will not matter in a relationship?
How naive!Â*
If this means a lot to her, and she means a lot to you, then why dont you give her religion a chance? Listen to what her religion is about, take down points and think about it. If you really feel that you still have an issue with it, then you can list out point by point what you are against and why you cannot convert. But, at least, she should appreciate that you gave her a chance.
In the end, the issue is this: Your girlfriend obviously feels strongly about her religion. Whereas you have already said you dont feel strongly about your religion. If she is willing to break up with you about this, are you also willing to break up with her about this?
If you are, then go ahead, don't convert, break up. It's not love, someone else will come along who is better suited to you.
Keep us posted on what happens, okay? Peace!