This is yet another special "right" for the perpetually aggrieved. Decent soldiers are prohibited from wearing their uniforms for political events. Those agitating for gay "rights" are the exception to this rule.
I also thought they were supposed to uphold a certain decorum while in uniform. No PDA, no public drunkenness, etc. Seems to me just being at, let alone in, a gay parade would be demeaning to the uniform.