Doesn't matter on what relationship is, if someone cheats on me once they are a cheater in my books and there's nothing between us. You can't repair the trust after that. Though, honestly I've never been in such a situation and can't speak from direct experience.
Their past however can be accepted depending on the circumstances. For example I would look differently at cheating on the way out of relationship through a period of separation than a malicious form of cheating to "get back" at the partner.