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Dating is a tricky game. Finding a person with whom your wavelength matches, and around whom you feel you can just be yourself, talk about anything, and not be worried about being judged, is not as easy as the romantic movies and TV soaps make it out to be.
So if you feel like you both are getting serious, then talk to your girlfriend in time and sort this issue out. Put your best foot forward; be soft-spoken, courteous, well-mannered, chivalrous, and respectful.
First and most importantly, I see major trust issues in your future if you both think the other is brainwashed.
As for deciding to marry someone who is not mormon, here is how I made the decision. I met my wife at the age of She literally showed up at my apartment one night, wholly unexpected.
There are a million fish in the sea and it makes no sense to choose one with whom you are not religiously compatible.