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As far as her being an adulterer goes, it's not something I wouldn't expect from her. She did lose her virginity to a married man so I don't think it odd of her. And tbh I don't see it damaging to her character either as weird as that sounds.
Spoiler for Gilmores:
Thing is though, she was supposed to have learned from how that last experience went. Everyone got hurt, and that was the moral of the character arc.
Now, I can see Rory with a married man, but I couldn't see her A) cheating on someone herself and B) accepting that she's Logan's other woman. For god's sake, she loved the guy and she refused to stand for that bull**** at the height of her feelings for him.
Rory pursuing any other married man while she was alone fits. What they depicted did not fit for me. It was just an excuse to get Logan back in the series for fans.