Ok, I'm not looking for judgement, just an opinion to a hypothetical situation:

Situation:
Two adults are in a normal, closed, hetrosexual, long-term relationship. We'll call the man M, and the woman W.

M went to a party without W with one of his friends (who by the way hates W) -- we'll call her H. M gets drunk with H and cheats on W with her and a few others at the party.

Simplified:

M = Man
H = Man's Friend
W = Man's Girlfriend

M cheats on W with H and random party people.

Aftermath:

M realizes that what he did was wrong and apologizes to W. W says that she is willing to forgive M and continue the relationship, but has a hard time trusting him from then on -- and kindly requests that M no longer hang out with H if he wishes to continue their relationship.

M thinks that this is unfair, because he is very close friend's with H, and doesn't want to choose between H and W. W finally cracks and decides that M and H can be friends only if H apologizes for what she did with her man.

H will not apologize as she says that she has done nothing wrong. M backs her up saying that the blame is his, not H's. W is of the firm belief that since M did not rape H, that H played a part and if H wants to be a part of their lives, H should have to shape up and be kind to her and apologize.

Question:
What do you think? Do you find your empathy swayed one way or the other?

I'd agree with W about fault. Both M and H acted consentually, if inebriated, and both/neither are responsible (depending on your views of responsibility of acts while under the influence), not just one or the other. As for apologies, it'd probably be something I'd only be able to decide knowing M, W, and H personally. Making H apologize probably isn't going to do anything except increase animosity since she doesn't want to, and forcing it won't really gain anything since she could just say it to get everyone to shut up, leaving everyone in a state of quiet, or not so quiet, distrust.

In W's position, I'd politely and civilly talk to H and find out why she thinks she didn't do anything wrong, and try to convince her, civilly, otherwise, and let her make her own decisions.

Of course, the biggest issue is M and W's trust. If W can't trust M anymore, then the relationship isn't worth persuing, regardless of H. If W can, in time, honestly trust M again, then that's what they need to work on privately (H was not a root cause, at least as far as I can assume in this hypothetical situation). Knowing why M cheated on W, and working that out, is more important than H not apologizing. H apologizing is only needed for W.. but H hating W makes W unable to trust H, so it really doesn't matter what H does (even if H apologizes, they don't trust each other, so she'll never believe the apology is sincere anyway).

Do we know this wouldn't happen again with someone else whenever M gets drunk? Do we know this wouldn't happen again whenever H can get any influence over M? Is M secretly/unconsciously looking for a "better deal" over W, and H (being such a person) happened to be there with lowered inhibitions?

IMHO, at least.

What Jonathan said. M can't expect the other letters in his alphabet soup to get along.

I'd say W is right. I'd further say that I don't think M and H should continue seeing each other while M would still like to be with W, or at the very least have some considerable cooldown period.
I'd also expect M to cut down on alcohol intake.
Other stuff I thought about has already been mentioned.

W has made a very generous act for still being with M and still trusting him. He should be thankful.
Basically like Trent Gamblin said:

Is H > W? If so, I'd say M->H.

More proof that the relationship is doomed. If you really are committed, you never not back up your girlfriend, even when she is as wrong as can be. And this isn't even a case of her being completely irrational. If she wants the woman to apologize, then the least you can do is honor that request!

It sounds to me that the man should just hook up with his best friend and forget about his girlfriend. And then when he finds a new best friend, hook up with her instead.

I expect to see you, your best friend, and girlfriend on the Jerry Springer show soon!

LMAO

This is not Algebra. I've named M Bob, W Alice, and H Eve.

Everything Matthew said is right. Especially the part where Bob decided to stay with Eve instead of Alice.

Wherein and for whom lies the dilemma?

It depends whether you are M, W or H

Now, seriously, forgive what has been done, but end the relationship. End as friends or enemies, but end it. Once a dog tastes human blood, you sacrifice him.

[piccolo]
stay wit W only if you can get somethn out her and contnue your side project wit H. maximize your profits!
[/piccolo]

I felt his response was too long delayed.

that is his definition of a standard relationship. And obviously their feelings in this situation are affected by how they conducted themselves.

So don't try to be a trailblazer here for open relationships.

Also, the question of asteroids hitting the earth is not relevant to the question asked by the OP.