As a student of psychology; believe me, we ain't immune. It is 100% not the same thing giving a diagnosis than to receive one. Even with experience.
We are taught to empathize with the patient. Harley wanted to believe Joker. It is factually impossible to force someone to change, only the willing do that. Joker knew it and took advantage of it. Then circumstances played in his favor when Batman decided to be a bit more brutal than usual, leaving credence to what Joker said to Harley.
So Harley was the perfect subject for manipulation: Someone inexperienced, tasked to psychoanalyze the second most dangerous mind in gotham after Batman himself, willing to believe whatever her patient said, and said patient by circumstance being shown to be right in her mind, atop of an already sick mind. Her downfall makes perfect sense.
As for constantly being put up with a toxic relationship, that's even more complex and not something I'm comfortable talking about here. But yeh, it's not nearly as cringe as people make it out to be, and it's in fact uncomfortably realistic.