Active duty US Miltary personel are forbidden by the UCMJ from publishing political opinion statements. This is either a faux US Marine blowhard or an active duty idiot.
They do it all the time. I do it on this forum. Of course, you'll not see the name "Drew68" on my uniform or anywhere in my service record.
What most of us wisely refrain from doing is signing our political opinions with our name, rank and command. That's where real trouble can happen.