You should not have to delete your high school friend because your therapist is uncomfortable over this (and it is her issue). If she is so concerned about your privacy, tell her you blocked your friend's mom so she can't see your posts. You are probably right that she is more concerned about the aprn's privacy, but if she won't admit that, I would just address her stated concern if that's something that bothers you. Otherwise, I wouldn't even block the aprn and just tell your therapist you're really not concerned about the aprn seeing your posts and doubt that would happen anyway.

Your therapist's response would bother me a lot, including at the grocery store. They are supposed to take the client's cue, so if you acknowledge her and say hello, she should do the same, not act horrified and scurry away. How awful that she would rather make up a story about not showering (twice) than to say what she really thinks.