I once had a girlfriend who equated masturbation with cheating.
I think you have an uphill battle with this one. Either she isn't attracted to other people when she's in a relationship, or it is so ingrained in her that thoughts are the same as actions and that "bad" thoughts are sin. Ala Jimmy Carter's lusting after another woman in his heart. (man, am I showing my age here)
To be effective in persuasion, you first need to intellectually and emotionally meet the person where they are at. Find common ground in the argument. You don't need to totally agree with their premise, but find parts of their argument that you can agree with.
Validate the emotions she experiences when she finds you looking at someone else. Tell her that its understandable for her to have the emotions she has, and that it's ok.
But then, ask her if she thinks people should go to jail for thinking about killing someone. Ask her if people should go to jail for their thoughts? If her answer is yes. Run away. Very fast. If her answer is no, then steer the conversation to get her to actually say, "thinking about killing someone is not the same as actually killing someone". Get her to agree with the premise that thinking about something is not the same as doing it. Then tell her that, in the same way, thinking that someone is attractive is not the same as having sex with them.
Anyway, that's an approach I would try.
Me: 48 - Married, straight, male
Shiela: My wife.
Suzanne: My FWB
Adam: Shiela's LDR