What would you do? Tell the guy "too bad" and then watch him either blow up in the middle of an NICU? Is that really something you wanna deal with?
Or worse. Maybe you watch him slink away mad and then he waits around, follows the nurse out and goes after her later? The Nazi tattoo pretty much tells you this guy's not all there, and it's not like hospital security can escort her all the way home and stay with her for the next month.
Call the police and have him arrested? For what? being an ass isn't a crime. Have them offer the nurse protection? Did he actually make a verbal threat or did he just seem menacing?
Oh wait, you escorted him off the premises at a time when his wife was admitted and his baby was in intensive care? On what grounds? That he's a racist? That he said something racist? And then something happened to his baby when he wasn't there? Oops. Now you're looking at trouble.
What you're not getting is that there are a lot worse ways this could have come out. Instead, the hospital goes to the nurse and says "Yeah, this guy's a twit, but we have to deal with him. You're not losing any pay or any time, we just can't have you working on this baby."
That's the big picture.
They can simply tell him no, we cannot do that. If he has an issue with that decision, hospital security should be glad to talk to him. If your argument for allowing racist behavior is fear of threats or retaliation on whichever parties involved then hey let's just allow all racism to slide. We wouldn't want anyone to get hurt.
The hospital absolutely accommodated racism, what is there to dispute about that? I will ask the question again. If this sitaution was no big deal at all and completely within the laws as you keep suggesting. Why did the lawyer for the hospital get upset and have to intervene on a clearly poor decision?