Everyone is entitled to have their own "deal breakers". The only reason to get married or stay married is because one wants to. You shouldn't have to explain or defend your reasons to anyone. For me personally, cheating would be a deal breaker.
I say this because I'm the type of person who goes all in when I'm in love. If the person I was with cheated in wake of that then I can't think of anything else I would I have to offer for a second time around. Your best is your best!
Now if I were a neglectful, distant/cold, inconsiderate, unaffectionate, and lacked interest in the things that make my mate/spouse happy...etc There might be a slight chance I would forgive them having accepted the fact my ignoring her needs contributed to making her ripe for an affair. Even with all of that in mind my spouse/significant other would still need to prove to me they want US to work out. I may have been wrong to ignore them but they were wrong not to end one relationship before pursuing another one.
Cheating is NOT a "mistake". A mistake is an "unintentional act". (forgetting to dot an i, cross a t, turning left when you wanted to turn right...etc) Unless "the other woman/man" looked just like you and lived in a house just like yours there is no way they had sex with them by "mistake". I'd be insulted if my mate called cheating a "mistake". - One man's opinion!