That's a stupid rule. I have two Facebooks, one with my legal name and one with a nickname. I do that so I can have one for coworkers with more open settings and the other for friends where I can speak more freely and has locked down privacy settings. A previous name of mine had been flagged, but my current one hasn't so far. Hopefully it stays that way. Let the drag queens live. Using their stage name hurts no one and protects themselves.
I can't speak to if it puts them in danger or not, but making them use their real names on Facebook is a really bad look for Facebook imo.