Picking your friends by their politics seems like a bad way to maximize personal well being, unless they insist on talking about it all the time. Indeed people who ostracise others because of ideology are often the ones who can't stop talking about it:

A fanatic is one who can't change his mind and won't change the subject. --Winston Churchill

Most people compartmentalize quite well and most humans are hypocrites. In the real world people with weird or "evil" ideologies can still make great friends and can be good people. And people with wonderful sounding belief systems can be horrible human begins. Don't underestimate the utility she may bring you and how much utility you can bring her by continuing the relationship.

Note that if she is into virtue ethics she may view severing your friendship over religion a breach of loyalty, not something she would do, which means you are sort of defecting. (;_;)