So someone's response to your hypothetical should be what "I don't believe in the things you're going on about, but Preach it Brother, my beliefs don't matter"?
It was not about preaching it, but about believing it in the first place.
Yeah, for many people it's a pretty big deal. That's their choice, but don't expect others to be appreciative of their intolerance. If someone presented me that kind of ultimatum, I would immediately end the relationship, and that regardless of whether my faith, or lack thereof, was something I was prepared to change, but simply because I don't want to be with be a person who would demand that of me.
In a game, I would like to have the option: "f*ck off and good riddance, then".