No, your T shouldn't terminate you for that. If you feel that the FB incident created some conflict of interest, you can talk about it with your T, and if you feel your T won't be as loyal to you anymore, then you have a choice of finding a new T. But your T cannot ethically terminate you because of what happened on FB. This situation doesn't create a conflict of interests provided that you don't have a relationship with that other person on FB other than being a part of the same support group.