OP, I once 'fell for' a married man. It was well known amongst his friends that their marriage was over but they were together for the kids/finances etc. It does happen and there are also many threads on MN that are testament to that.
No one knew how I felt. Not even my closest friends (who also knew him) because I was embarrassed about it.
I treated him as I did my other friends and only saw him within the context of our friendship group. Spoke to him, had a laugh, but never even came close to flirting, never spent any time alone with him, didn't sit next to him, didn't even go to the bar at the same time as him.
One evening, after going to the pub as part of the group, he tried to kiss me.
Now, I could have thought, "Oh, wow! This man likes me!" This man I'd carried feelings for for about 2 years by this point. But I didn't. I pushed him away, turned round and practically ran into my car, and drove away.
Because he was married. And whatever i thought I felt for him. I am better than to be messing around with someone else's husband. And I deserve better than to be someone else's 'bit on the side'. His action showed that he didn't have the strength of character to do the right thing. Either to make a full commitment to the decision he and his wife had made nor to walk away and become a single man in a position to date. He didn't respect me because he clearly thought I was the sort of woman who would be flattered and respond positively. I found his behaviour offensive, not flattering.
I have never gone off someone so quickly in my life.
You can't control your feelings but you can control your behaviour and I'm one of the, seemingly few, women who post on here who doesn't see the OW as a victim or passive but as an individual with agency who has made a choice to be in that position.
He's not the first married man who has tried similar and I'm pretty sure he won't be the last. And they've all been met with the same response.
What exactly did you think was going to happen?
You deal with it by reminding yourself of your worth and of what he is choosing to do. And then you work on yourself so that you're not vulnerable the next time one of these blokes tries it on.