How is his following his beliefs -- when not on duty -- a violation of that principle?

Or are you arguing that soldiers must check all of their beliefs at the door when they sign up and be automatons while serving?

Or are you arguing that when he's on the front line he's thinking that he may not shoot the enemy this time because gays are getting married in the US?

Hopefully your narrowmindedness and prejudice also would extend so that the army should have kicked Nidal Hassan out pretty much as soon as he expressed an interest in Islam.