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.
What they cannot do is advertise Well, I'm a Marine, Soldier etc and this political opinion or that. Or use DoD to further their goals/views.
They cannot wear a uniform to promote politicians, political rallies etc. Hence when Bob McDonell showed his daughter in uniform during his VA campaign (on a flier and i believe his website); he had the disclaimer that the US DoD was not advocating or supporting any particular candidate... it was just his daughter that HE was proud of.
Roger that. I read the full source article, without considering it is an anonymous blog. This supposed sgt c, got my blood up and I knee jerked my post. Thanks for the correction.