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A quick side-observation: The real purpose of forced loyalty oaths are not to create trust, but to destroy it.
The fascist saying "pledge loyalty or be fired/jailed" knows that an affirmative response doesn't mean anything, but that's not a primary goal.
Instead, they're forcing the remaining people to scar their own reputations in a way that makes it harder for them to self-organize. It seeds a doubt: "Even if this guy didn't really mean it, it still means they were willing to lie when their job/freedom was threatened. They say they're on my side, but... have they threatened again, and are they lying to me now?"
My point is that those very-visible outcomes aren't necessarily the most-impactful result of the policy.
Even without a legal framework, it happens sometimes, through various means. Ireland used to be an integral part of the UK, say, Finland used to be part of (imperial) Russia, and the Baltic states were part of the Soviet Union.
And it is always like that. The ones who benefit the most from armed society and those who have the least inhibitions to harm.
The US military relies heavily on contractors and civil service for logistics these days, it is basically non-functional without them. Unlike members of the military proper, civil service and contractors can walk away with very little trouble (other than finding employment, of course). Members of the military will risk court martial and other disciplinary actions if they refuse and may have their resignations refused.
Who maintains our weapon systems? Civilians. Who maintains the communication networks? Mostly civilians. Who builds our aircraft and munitions? Civilians. Who maintains our ships? Civilians. Who builds our ships? Civilians, but they're not very good at it anymore. Who maintains our nukes? Civilians, but they keep getting fired and rehired.
Stop providing power to US military bases in Europe (naval bases might be able to provide a portion of their own power from ships). Stop or slow walk fuel deliveries to air and naval bases. Don't provide the labor at those same bases (the Europeans working in those bases would quit on their own, this would require no coordination from any governments). What's the US going to do? Invade all of Europe to fight back? Send troops out to claim European power plants and infrastructure? And hold it how? The US military (as in the enlisted and officer corps) does not run their own logistics. The logistics are all pushed onto civil service and contractors, many, if not most, of whom would quit rather than engage in a war with our current allies.
If the scenario here is that US invades Greenland leading to an EU vs US schism, then it might not be Russia today vs EU today. It could be EU minus US support vs Russia with US support.
That'd be a pretty different dynamic, and pretty bleak for democracy.
Rhetorical question: Who would you rather be loyal to, (a) a man who grabs women, pays prostitutes to silence them, and has been convicted of multiple crimes or (b) all the people of Canada?
If the citizens of the USNA are smart, they will choose the latter. (Loyalty should be to a country, not to a leader - the latter concept applies only in dictatorships.)
Oh, and the Panama Canal will continue to be labelled "Panama Canal" on all my maps as long as I live, and there is nothing any president can do about that.