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

Superiors and any issues they may have.

Only the things that you want to see become issues.
Not talking about something is a sure way to turn them into an issue.
Don't talk about family? Prepare to see divorces.
Don't want to talk about race or religion? Watch your people clash over them.
Don't want to talk about feelings? Start planning the funerals of your subordinates suicides.
One of my best leaders said leadership is relationships. You need to be in people's lives asking personal questions. It's good advice.

Race, Religion, Nationality, Sexual Status, Ethnicity, Family Troubles, Feelings
and that other thing we don’t talk about – because we don’t talk about it.

Politics, religion, sexuality, financial recommendations with the following exceptions:
- you have the right to vote and the military has voting assistance to help you. What ever you do politically, it shall not be in uniform or otherwise representing the service. You do so as a private citizen. When in doubt ask your leadership.
- in the place or with the being you go to when you are cold, wet, tired, and hungry to gain strength, you have the right to worship (or not) as you see fit and have Chaplains to help you when you need it. Crom does not laugh at your Four Winds.
- you are responsible for your personal choices, reproductive decisions, and the consequences. Choose carefully as they can impact your career as a soldier, your health, and your life for the next 18-26 years. If you want help with these issues, we have a plethora of people in multiple health, spiritual, legal, and social vocations that can help you before and afterward depending on your moral, ethical, And spiritual beliefs. During is on your own moral compass.
- if you are sexually assaulted, there is help for you and that will be the focus of the unit Command team. You may report it formally or informally, just ensure you report informally to those that are designated so that you can access services with out a law enforcement investigation or Command knowledge. Understand that the Command team is a formal report that will be pursued through law enforcement to its logical conclusion.
- if you care about your career and financial future, learn about spending, saving, retirement, and financial security. We have people at ACS that can teach you, to include the viability of the financial products you are being offered. Look before you leap and run the numbers.

Religion, transsexuals, and Trump.

Gossip in general and anything about senior officers or NCO. Politcs, religion, race, sex

Politics, religion, sex.

Leaders should not discuss politics, religion or their sex life around subordinates. Familiarity breeds contempt.

I would assume that you shouldn't talk about the leadership, politics, sex, or religion. Obviously there are exceptions like reporting sexual assault, the obligatory safe sex safety briefing, and informing soldiers that they have access to voter assistance if they'd like. Talking about the unit leadership is almost always bad. Essentially, if it's not pertaining to work and you probably shouldn't discuss it with subordinates.

A lot of this depends on the situation. If it's a group conversation I will be more reserved in offering personal feelings on some topics. But if one of my soldiers comes to me for one-on-one advice, I'll go a lot deeper into my own personal/political/religious beliefs. This isn't an attempt to convert them or anything like that but the notion that humans can separate themselves from who they really are is absurd. Who I am and what I believe shapes the advice I give (as it does with everyone).