This was a personal interaction, not in a professional context but: "I've done a medical degree, I'm sure I could pass a quantum mechanics exam with a couple of days' studying" while I was revising for my finals was a good one. Had a "You're not a real doctor" at a party once as well.
A question from Reddit that I'll answer here:
"What's the most unhinged thing a doctor has said to you with a straight face?"