I think the thing in question is the sex. I know if my monogamous committed SO decided she'd rather roleplay sex with someone who wasn't me, I don't know if I could trust her anymore, even if it was "innocuous" because I take commitment very seriously. I would consider it emotional cheating.

But that's just my way of seeing things. OP, your girl might have not thought it was important because she doesn't see RPing with a trusted friend as emotional cheating.

There's a talk I think you guys need to have on where you stand on the sex thing. You may not find that you're compatible there. In which case? Good riddance and on to someone who respects you.