I'm going to take a shot in the dark here and suggest that even if your anecdotal evidence isn't just you making something up, in none of those cases were nurses/doctors FORCIBLY reassigned due to their gender, religion, or ethnicity. They voluntarily stepped aside, or the requests were made before anyone had been assigned to the patient's care.
You're seriously reaching here.
Nurses and doctors being told to comply with patient requests is a common thing, regardless of whether the request makes sense or not. Refusal to do so would only be on the grounds that it might hinder the patient's treatment.
And again, other than feeling offended (which isn't actionable) what actual harm is there to the nurse for not handling this particular baby?
The guy's request is crap. The guy is a prick. But again, none of that is the hospital's fault, and their honoring his request to avoid trouble is not grounds for legal damages. Frame it any way you want, but the result is the same.