What topics should a military leader shy away from discussing with or around subordinates? Why?

A leader should be willing to discuss almost anything with their charges. That said, the SCOPE of that should be limited by a lot of factors.
I hear a lot of people mention religion. If a troop asks a question or wants to discuss moral or ethical implications of religion of military decisions, we can direct them to SMEs like the chaplain, or point them to the applicable regulations. We just have to remember that "personal opinions and professional opinions don't always coincide."
That's the real conflict. We are trying to maintain a professional working environment, therefore we should MINIMIZE (it's nearly impossible to eliminate) distractions. Religion & Politics are the two classic examples, because they are about "belief" systems. We generally can't change people's minds with logic or arguments (at least in the short term), therefore it is better to just avoid them.
The other ideal is the Private vs Public divide. Whatever you put out in public becomes public forever, therefore it is a good idea to retain some semblance of control on your personal information, regardless of what it is. The military and the CoC already has LOTS (possibly more than you would like) access to your private life. Do you really want to give them more? That goes up and down the chain.

Politics, especially toward executive branches, when leaders speak poorly of the executive branches or the lower command structure it sends a message that its ok to be disloyal, and it is outside of the military professionalism required to perform the mission. Also it could lead your subordinates into a legal situation with UCMJ.

Once in awhile on here, I do find thought provoking topics...hat is clearly one...I haven't a clue as to what to suggest, however, nevertheless, it is certainly thought provoking, notwithstanding, certainly...I've gtta give that one a good deal of thought...I read a good deal of what was sent in here...beyond that, for the moment at least, aside from all those topics already !mentioned, I quite honestly don't have a clue, to be candid...as I'd said, lemme give of some thought....