The author of the article is talking about specifically actions occurring fully within the confines of how members of the military carry out their duties. A superior officer can order one of the soldiers in their unit to guard something. They can order them to carry a rifle while doing so, and can order them to do it wearing a mask. Asking that soldier to force someone not in the military to wear a mask or undergo a strip search may be illegal (I honestly am not sure and it's a moot point to this discussion).

TSA agents are not members of the military, though. They are employees of the TSA, and the relationship is not bound by the Uniform Code of Military Justice, but to an employment contract and normal civilian laws around labor.

I think you got too focused on the details of my analogy and ignored the point of it: just because everyone gets taught how to do something, doesn't necessarily mean that thing is okay to always do.

I think the point of the "taught" point in the article was to reinforce that mask wearing was not a novel question in the context of "is this an order that a military officer can give to a subordinate?", nothing more.

The page won’t load for me so forgive me if I’m missing context for this analogy. But on its face it’s clearly not analogous: training on how to wear a mask is an action taken on one own’s body, strip searches are performed on another person.

Granted, out of context I find the quoted reasoning equally unconvincing: servicemembers (presumably military?) may also sometimes trained on how to commit suicide in the event they find themselves in circumstances with greater risk of peril, but that doesn’t mean it would be lawful to arbitrarily order them to do that.