You're really trying to say the government would let TSA go on strike.

For all I know maybe they are already prevented from going on strike. But, since they are there for "safety" and are front facing customer "service" reps, a strike to be paid like Flight attendants would be plausible.

If they are/were "union brothers" would I support that?

Rolling stikes like the French rail workers( happened to me 3 times over the years while on vacation in France). I didn't raise my fist in solidarity, was I supposed to?