If you're correct (very possible but by no means certain,IMO) then a less than honorable discharge may well be appropriate.If not,then counseling should have been the first step by the chain of command.
I don’t know who found out about his postings, or how his command was made aware of them. I have no doubt, however, that when the command was made aware, that he was counseled. Relying on the advice regarding the disclaimer no doubt contributed to his continuing. At that point he was (and should have been) hosed. I think the OTH had more to do with his response to the counseling than his postings on FB. Stupid is hard to fix, obdurate stupidity even harder.