How would you handle a double standard or disregard for Army Regulation?

There is a back door here. It's called Social Actions. At least it was in the AF.

I honestly respect the hell out of your Soldier, and if he were mine, I would back him up all the way to wherever it needed to go, as you are doing.

It's sad that there has to be a differentiation in responses to capture the reality of the double-standard trouble he could find himself in, while acknowledging he did the right thing and is now intentionally behaving in a way that highlights the blatant double standard enjoyed by the unit leadership.

Maybe you could try accompanying your Soldier to a couple of the violation hot spots, and when he makes an on-the-spot correction, you are there to back him up if he gets resistance, or if it's a leader, you can highlight the double-standard right there on the spot. Of course, if you are present, then you should probably be the one to make the correction instead. Something like, "well you know sir/1SG/CSM, that is the rule, and just the other day I saw a junior Soldier smoking inside the building. When I approached him about it, he cited seeing you violating the same policy, so he figured you had approved it and he was ok to follow that example." I don't think it requires a nuclear response on your part, just one that forces them into cognitive dissonance.

I’d write him for an AAM. Kid has guts. We need troops with guts.

Something a lot of people do really bad at is watching their own lane. By that I mean, "well so and so is doing xyz, why cant I?" They base all of their problems and happiness on someone else's actions. Just because someone else is in the wrong doesnt mean you intentionally break the rules. That will get you no where but in trouble. While the Soldiers chain of command is wrong, they still hold UCMJ authority. Would it be hypocritical to administer punishment for a violation of the no tabacoo use rule? Hell yes. Is that going to stop them? Probably not. Will the Soldier still be guilty and have punishment imposed? Yes. You need to have a tough talk with your Soldier. Especially if they are yours, you're the NCO, you set the standard. Who gives a shit what everyone else is doing? You run the show.

That Soldier is definitely E4 Mafia bbn and will no doubt receive the Iron Balls Award from his fellow E4's.
If it is a serious battle the Soldier wants to take on though, he'll want to do it by the book, and run it up the chain of command until he finds an allie.
This is one of those times you really need to take a step back and think if it's a battle worth fighting.

While appalled at the poor examples of leadership, I have to say, choose your battles. This is is a bad path to go on. The vaping, "in you face", violation at the, is just begging for action. Is the soldier wrong? Yes. He knows he is in violation, but is doing it anyways. He has clearly crossed the line of "Insubordination".
There are better ways to get your point across. Bring it up in In-service training, or NCO development classes. You know "Some" or "A lot of" individuals seem to be violating this policy. Not "CSM" and the "LTC" are violating, so why should I?
It was mentioned by CSM Richard StCyr , to talk to them privately, about the issue. It is amazing how well this can work, if done properly/diplomatically. By bringing the contradiction to them privately, you have an opportunity to make them aware of the "confusing" policy standards they are presenting, by not following the policy themselves.
A good leader, will remember the next time they are out and about. A simple nod might remind them again in the future, should they slip.
Unfortunately, we all know that not all military leaders are "good leaders". Some can be, plain and simply, vindictive. Especially when being called out. This is where "choosing your battles" comes in. Is it worth your career? Is it worth the misery, that can be produced? and is it worth the potential non-judicial punishment, in the case of the openly vaping just because the leadership is violating the policy.
It's kind of like calling out the half pushups the PT studs get counted, while the not so popular soldiers are don't get counted, no matter how low they go. What's the point if nobody is listening?

Was either the LTC or CSM made aware of the soldier’s inquiry regarding the apparent double standard with regard to tobacco use inside working spaces? Did they realize the “standard” that they were setting for their troops?

There is usually a fairly logical reason for those regulations being in place and acting counter to them should not be taken lightly, regardless of how insignificant they may seem. Once personnel start disregarding the “minor” policies and regulations they will eventually transfer that behavior to the more significant ones. If a service member doesn’t understand or disagrees with a regulation or policy, they should feel free to express that in a professional and respectful manner. I’m okay with people asking “why?,” as long as they continue to follow the regulation/policy until the appropriate entity determines that it should be changed.

The double standard set by the LTC and CSM is troubling. Hopefully, it was just a case of them not realizing that their behavior could be perceived as setting a double standard. If they are aware of the perception and continue on with the behavior then I would suggest kicking the problem up the chain in one form or another. I don’t know if the Army does command climate surveys like the Navy does, but if so that might be a way to inform the upper echelon of the issue with some level of anonymity. Or when a senior leader visits, they usually give Soldiers/Sailors/Marines an opportunity to ask questions and the regulation regarding tobacco use in the work spaces and the associated double standard seems like a reasonable topic to bring up.

This sounds like a time for a good NCO to ask to teach a class on the subject of AR 600-63 Paragraph 7-3a at the Bn. Level on the BN. Training SCH. make it fun, make it truthful, and don't mention names directly or rank. Worst you can do is get told not happening and don't mention it again. That would pretty much let you and Command know how this will be playout moving forward.
This is a little like Seat belt laws not everyone agreeds with it in the begining so it is hard to enforce and will have many up and down battles. I personally do not agree with the regulation howerver i don't write regulations i educate Soldiers on the regulation and enforce them. I really can't say how i would handle this situation because i don't have a dog in the fight right now, but would take the teaching a class approch 1st.

People tend to follow the example that is set for them by those in charge. Its pretty hard to enforce rules against others that You don't follow Yourself, lead by example. If, as a leader, Your not going to enforce the regulations You are charged with being responsible for then don't expect compliance ! If You poor example backfires on You, well that could have been prevented and the responsibility is yours as a leader !

Lol your soldier is absolutely in the right to point out double standards. If the attitude is to check down, go above them in the chain.