As one who has concluded that they have enormous trust issues, yes, it would be a deal breaker. I mean, I don't feel as though I could engage in the relationship the way that would be healthy for either party, and it really is a huge betrayal, so...yeah. "Emotional" cheating is sort of a gray area. As a self-described asexual, I can see it being a bigger deal for me than otherwise, but, as has been mentioned, the defining factor here is intent.
If they actually act on whatever it is that they've got going on, yeah, I'm done, but if they don't, I can't say I'd be too put off. I mean, I am of the belief that people can have feelings for more than one person at any given time, and it's something that doesn't bother me to any substantial extent. However, if action is taken, even with a lack of sexual contact, I can't say I would be in any way pleased/indifferent.