Their is a DoD directive that gives explicit permission for service members to express opinions in letters to the editors. They may identify themselves and the rank that they hold so long as they're clear that their remarks are not being made in an official capacity. I would think that a Facebook page is very far removed from a letter-to-the-editor, IMHO.
"I would think that a Facebook page is not very far removed from a letter-to-the-editor, IMHO.