For the most part his actions, per that article, would not be illegal under the UCMJ (though the bumper stickers are something of a gray area in that they are not just political speech but overtly critical of the President), but obviously we are getting a self-selected list of his behavior chosen by him and Fox News. Moreover, notably, he has not been charged with anything, nor given an Article 15.
I can only assume that all of this laundry list of his behavior (which also includes retweeting a tweet that said "Lordy, Lordy, its lovely human Tuesday. The lefty loons and Obamabots are out in full force") is indicative of his generally being an obnoxious loudmouth, which is normally not the way to win friends and influence people in the workplace.