How about I break up with my girlfriend because she is not religious?
Why does a girlfriend need to be religious?
I'm a christian and I strongly believe in this
I'm not sure that you should break up with someone just because they are not religious, but if you're really not interested in her because of this flaw then it is pretty serious. You should find someone that you feel more compatible with and shouldn't keep her in a relationship if you're willing to break up with her.
I'm not crazy about her to leave her because of it.
That's fair and if you are unhappy with her not being religious then it is better to break up with her rather than attempt to convert her. You'll both be happier once you find people who are more accepting of your various beliefs.