Probably also wants to avoid possible Posse Comitatus hassles from lefty organizations, which would absolutely surface if active soldiers were found doing this. If the base had said nothing, and a soldier were found participating, the lefties would have called it "tacit approval" and flogged them even harder. I suspect the base absolutely supports the Minuteman actions, and shows it by keeping them from getting shut down as a "side benefit" of a Posse Comitatus lawsuit.
Protection of our Nation's borders is supposed to be one of the duties of our military services..
Probably not. The current military leadership is afraid of CNN. A bad report on the nightly news now ends careers. It's all about PR, you see; it's more important to look good on camera than to actually do your job.
Where have the warriors and patriots gone? They've been replaced by CYA bean-counters.