Any ideas about how I can gently and politely decline his FB request for my phone number as well as the likely subsequent kind offer to come over for a meal (with nice people who I really don't know)? Thoughts? Ideas? 5/5

Throw some legalese at him and pull the same thing I always tell my kid--BLAME ME (or in this case your employer). "I would LOVE to, but per Doctor's Legally Binding Rules of Engagement That Lawyers Are Serious About (or whatever) I simply cannot accept. but I checked, we can stay FB friends, yah!"

He should be able to understand a polite refusal saying you don't socialize with patients.