This article from Femininste says it better than I could ever say it.
Of course, there are caveats in the relative lack of morality in sleeping with married men- it could be an open marriage, it could be a French divorce. But when a woman has proof in the form of an email or a letter that neither of these options are the case, the only thing I think is appropriate for the other woman to say or feel is “I’m sorry.” Anger towards the wife? No way. Pissed off that the wife called you out? Just desserts. Anything other than “I’m sorry” is arrogant and pretty rich and smacks of poor character.
Or, in the words of the OP, “If you show zero remorse for being involved in something that hurts someone else, you have a problem.” When you are with a married man, it is never innocent, justified fun- someone is getting hurt. As such, I have a very, very tiny violin I can play for any woman who tries to make excuses for her actions. I do think, however that it’s ok to sleep with someone before you know the deal, but once you know what is going on, you owe it to yourself and his wife to GTFO. This comment, especially, nails everything I could ever say about how the wife feels: “Know who defines cheating in a relationship? The person being cheated on.” You shouldn’t get mad at her for calling you and her husband out for being deceptive POS- she is the one coming from a position of pain. Accept your (admittedly shared) role in destroying a marriage, apologize, and try to do better for yourself and for another human being the next time. You might actually grow.
Finally, and this is the crux of the matter for me, cheating is a public health issue. As I have always said, and as this comment on the OP so eloquently states, if you are in what is supposed to be a monogamous relationship and having condom-free sex, and your man is not telling you about his side piece(s) out of “discretion” and “not hurting your feelings”, you are unwittingly being exposed to STDs. I remember one sister whose husband didn’t get an STD but got staph because her husband’s new piece had suspicious boils that he, in the heat of passion didn’t care about. Men are generally asymptomatic when it comes to yeast infections- sometimes his girlfriend gives you one. I can dig poly relationships and open relationships, but personally I care too much about my health to “share” a man, and being forced to do so out of deception is unjust and unfair.