Specifically, you might want to look at the Punitive Articles. In there, you'll find things like Article 88 which restricts to a degree the free speech rights of commissioned officers to express a critical opinion about President, the Vice President, Congress, the Secretary of Defense, the Secretary of a military department, the Secretary of Transportation, or the Governor or legislature of any State, Territory, Commonwealth, or possession in which he is on duty or present.

However, you won't find anything in the UCMJ prohibiting a military member from expressing a religious opinion. It's amazing how the PC bigots are so quick to slap down people who express religious views they disagree with, often to the point of demanding they be fired for doing so. Bigotry is as bigotry does. Don't tell me, let me guess, some of your best friends are religious. Yeah, right.