I wonder if her mindset is more on her cheating or both of you cheating. If you asked if she would forgive you if you cheated on her, would she? And if she says yes, is that honest or is that to try to "make her point"?

Cheating is straying from the relationship and essentially forming a relationship with someone else whether it is physical, sexual, emotional or what not.

I also wonder if she is testing your boundaries on the subject, seeing what she can get away with. I would hold off on marriage until you are 100% sure and if you don't see the relationship going anywhere then maybe break up. It's okay to have different views but her view on cheating sounds like a deal breaker for you.