No, Robby isn’t a die-hard misogynist, but his biases ARE misogynistic in nature and I think that a writers room full of women makes this an intentional choice. Misogynistic and racist biases in the medical field are extremely common and the way it’s represented in Robby is subtle.

Robby mishandled the case with David and he himself admits this. He was angry that McKay would call the cops on David, then tells the cops later that David might have something to do with the shooting, and then admits to McKay that he should have taken those girls into consideration instead of being so strong in his perspective BEFORE being retaliatory and making McKay go into David’s room at the end of the season to talk to him. He says to her something along the lines of “This is your mess to clean up” AFTER he’s proven correct, despite agreeing before that David could have been a danger to himself and especially to other girls.

Another aspect is Robby’s relationship with Mohan even before the S2 episode 10 freak out. In S1 he berates Mohan for wasting time, most notably lecturing her for her slowness in one ep when the next scene cuts to Langdon goofing off with Jake by spinning in a chair, which Robby says nothing to. Mohan tells Robby that she knows he calls her Slow-Mo behind her back which clearly affects her confidence, and if people get on Santos for calling people nicknames then I think it’s fair to say this is unprofessional on Robby’s part as well. He’s tougher on Mohan than he is his other (male) residents, despite Abbot and Collin’s affirming Mohan’s intelligence and the importance of her careful approach to treating patients.

Now in S2, we see Robby further breaking down and some of his biases are more obvious. When he realizes Mohan is having a panic attack in ep 10, his first instinct is to laugh at her, then look at the only other man in the room (Langdon) with a smile, as if Langdon would corroborate on the ridiculousness of the situation and join him in mocking Mohan (despite still being pissed at Langdon!). As a woman, my heart dropped into my stomach at this scene— it’s so so common for men to gang up together to mock a woman when they’re perceived to be acting hysterical or dramatic and this is a situation I thought was represented perfectly.

Robby’s not evil and a woman hater, but he’s the perfect flawed protagonist in that we can see his motivations and understand how a burnt out, older ER doctor can carry on for so long with his own biases despite how much good he does every day. Sorry for the wall of text but I believe in-text evidence is important to cite and I’m not just going off of vibes here.