Sure, we do it here all the time. The problems can start when you become more involved in public politics instead of just talking about it at the bar or on AW. I think he is treading far into the gray area, not specific enough with his politics or statements to get hammered yet by existing rules but with a single statement or action he could cross the line easily, especially if he started speaking in public. With this type of action though I would not be surprised if the DoD revised it regulation sooner or later to encompass other stuff like this. Then again they just might let local commanders exercise their discretion in cases like this, unless it causes too much controversy.
+1 for this. I don't think his facebook postings were necessarily the thing that got him in hot water; the fact that his facebook postings led to get him an invite to comment on TV is what's inappropriate.