Can't speak for Woody, only myself. The answer to your question is yes. If/when I have occasion to let my subordinates know what my standards, expectations, etc. are, I let them know that I don't brook anything that detracts from good order and discipline. That includes alcohol-related offenses, and yes, even sexual misconduct (whether homosexual or heterosexual). I don't single out anyone for any particular sin or conduct that are against the bible; but when such sin or conduct detracts from the performance of the mission, and/or affects others around them, because I've already identified my expectations and standards, I can then charge them with Articles 90 (in Woody's case, Article 91), 92 and 134 of the Uniform Code of Military Justice. At the very least, at this point, I can issue them an Article 15; or subject them to court-martial if they refuse the non-judicial punishment.
In jobs where I don't directly have subordinates (otherwise known as "staff"), I have had a sign hanging over my desk that says "I am a Christian; you will hear me say things that reference Christ. If that offends you, then don't ask me to talk to you." I've never had anyone ask me to take it down. I hung this so that if someone had ever complained, I can always point to the fact that they had foreknowledge, and therefore can't claim "surprise" when I do reference the Bible or Jesus.