I don't exactly have a lot of sympathy for this woman. Or any one caught up in this mess.
"My institution has a morality clause in all contracts."
Choose to sign the contract, choose to sign up for the site, choose to (maybe) have an affair?
Aside from my lack of sympathy, I don't think this woman has done something unforgivable, or that makes her "unhireable". People make mistakes all the time, shit happens. I have to say that if your in a place where this "matters" then you need to address those issues, and move on. Its a big world, your an adult and free to make your own decisions both good and bad.