I don't think that would be okay with a therapist you have seen that recently. It seems he's pretty clear about there needing to be a boundary between you. Chit-chatting occasionally is different that being privvy to his entire FB account and constantly involved that way in he personal life.

I do FB with two old therapists, but we are talking about therapists I saw literally decades ago (20-30 years) who live far away and our lives are completely separate and have been for ages.