"...but if the person is behaving badly in the main relationship, that can be a problem with little or no relevance to the third person's role."
I understand where you're coming from. For most friendships, I agree, that 3rd party has no relevance, however, when the 3rd party is jealous of the time spent with the relationship partner, then they are a very relevant part. They add to the emotional withdrwal by causing the person to feel they are violating the friendship. It's a fine line, there are definitely cases I wouldn't worry about, but it's that one where the 3rd party suddenly has a voice in the current relationship that's the problem. By all means if the person having the friendship with the 3rd party is seeking out a safe place because the relationship is a bad one (abusive), then the person should seek help. But in a normal everyday relationship, a 3rd party should have no voice in the relationship. Why hide things? If it's a good friendship, the significant other will understand that.
Emotional infidelity is cheating in my opinion, not because it happened to me, but because of what a romantic relationship is, it's not just sexual monogamy, it's a trust and confidence relationship. If you don't trust the person you're with, if you don't feel you can confide in them, and you don't tell them that, and you seek out that trust / confidant somewhere else while leading the one you're with to believe everything is ok, you're cheating on them plain and simple. If you're in a relationship things like that need to be out in the open, not hidden behind the guise of "friendship." I'm not saying they should necessarily stay in the relationship if they can't confide, but at least be honest about it, bring it out in the open and just end the relationship, don't play both sides of it.
I've been on all sides of it, I've emotionally invested with others and withdrawn from a relationship, I've been the 3rd party, and I've been the significant other who's lost their partner due to the emotional withdraw. On all sides of it, there is some responsibility. As the friend, if you truly value your friendship and it is a good friend, wouldn't you encourage the person to either work things out with their partner or at a minimum be honest with their partner? If for no other reason than your compassion for your friend? If you're the partner and your significant other is withdrawing, don't you have a responsibility to address it and get it out in the open? And if you're the one withdrawing, don't you have the responsibility to relate to your partner that you don't feel you trust them?
So you say that no sexual contact means no cheating and that the 3rd party has no relevance...then what's the line that makes sexual contact cheating? Does the 3rd party have relevance there? As much as we don't want it to be the same, it is. The person is doing something outside of their relationship that should be part of the relationship, not the friendship.
I appreciate the opposing view, I guess in some way I'm trying to work through it all in my own head, and opposing views are always helpful when trying to work out your own conclusions.
Just my $1.50