If someone does not confess or cheats multiple times or even worse has an affair I believe that is one of the worst things you can do to a person short of the obvious things like murder, violence, etc.
For me personally there can be no forgiveness. I'm not the moral police though, everyone is free to forgive as they want. If someone is cheated on and feels that its not a show stopper then that's their choice, I'm not them. This is very much just a personal thing, for which there can be no forgiveness. Divorce and separate lives is the only option. I would of course still co-parent my kids with them and be civil (similar to how I interact with my kids teachers) but any emotional attachment would die. I would tell the kids why we are divorcing when they are old enough. This may just be a me thing its very easy for me to do the whole "dead to me" thing and just move on.
Out of curiosity, why is that particular situation a red line for you?