Well, just look at the fallout from the few times other characters have had storylines involving cheating. Oliver Queen is the closest you've got to a major character with that, and clearly some fans despise the more egregious moments of that. And he's arguably been slowly transformed into a character you could *maybe* expect to have that trait, so what may be debateable about him probably won't apply to other heroes.
Probably the biggest problem with trying to pull off any cheating storyline (in any medium)is that you have, at minimum, 3 separate characters who generally all have to be treated somewhat respectfully, or have at least one character be a clear cut villain, for people to accept it. Probably the only cheating storyline that I've seen work where everyone still kind of likes all participants would be James Gordon, Barbara Sr., and Sara Essen, a trio of supporting cast members, two of whom were only minor additions to the mythos at the time of the cheating. In contrast, I don't know a single fan of the characters Jesse Quick or Jade who approves of the storyline where they were involved in infidelity, and it's kind of hilarious just how little patience people have for Lois Lane's other love interests period.
There's also the simple fact that a well-written infidelity plotline threatens to subsume all subplots in a characters story.