We'd have to imagine an ATL where by some date in the 1970s Sweden had become a feared and despised pariah nation. This is even with the USA meanwhile also going down a parallel path of outright dictatorship, to shut up the vast numbers of American citizens who would have quite a bit of sympathy with Sweden's OTL official position--but it is not enough for the USA to be an authoritarian dictatorship ourselves; if the more powerful nations of Western Europe despised both Uncle Sam and the ATL Swedes, they would first of all break the NATO alliance, or rather reconstitute it as a wholly European thing and send the Yankees home (or give them asylum, those who didn't want to go home to such an America) then handle the regime change wanted in Sweden themselves.
With Sweden being united with similar capabilities to OTL, anyone trying to force unwanted change there would have tough sledding--one might think therefore the NATO European nations call on the USA with its vast capacities, but of course OTL we were deeply bogged down in 'Nam. No telling how things would be in an ATL but probably not being tied down in SE Asia means the region has already gone Communist (which might help explain a right wing dictatorship in the US to be sure).
But if Sweden is much hated and feared in Europe, presumably it is different than OTL, by a lot. On one hand, maybe considerably more armed and fanatical than OTL; on the other, would any regime in Sweden so despised outside it be capable of the sort of arms the Swedes made OTL?
And if Sweden has gone so wrong the nations of Europe would even consider pulling a Western version of the Brezhnev Doctrine and invading to impose some order more to their liking, facing the steep cost of it, would Sweden itself be united in its vaguely imagined wrongheadedness? Might it not be itself a fanatical regime barely able to suppress opposition which would turn on it immediately if foreign troops were invading?
It is just plain silly to suggest even an American President, even one as weasel-like as Nixon, would seriously expect even Americans, poorly informed as we tended and tend to be, to follow a trumpet call to invade Sweden just because the government and presumably a majority of free democratic voters there share an opinion or three with millions of US born and raised anti-war protestors in the USA. Might be different if the US regime itself is a dictatorship arising precisely to silence and repress those American protestors, but starting with slapping the Swedes down is completely absurd.
The elephant in the room is that the other European powers aren't a lot less "guilty" than Sweden would be. NATO did not actively and usefully support the US adventure in Vietnam either, certainly not with troops. (Australia, I believe under SEATO auspices and in general alliance as well as having regional interests, did send some troops to Vietnam). And plenty of their citizens enjoying democratic freedom also had what ranged from reservations to outright opposition to US policy.
If the European nations stand aside and let Uncle Sam declare a cage fight, just US against Sweden, they are setting themselves up to be taken down one by one in turn by the mad American gorilla. (Assuming the mad American gorilla is not deranged and disintegrating itself due to the strong opposition of repressed US former citizens now subjects threatening to fight a second American Revolutionary War to overthrow such a high handed, headstrong, and idiotic regime). If in fact the USA were crazy and stupid enough to take such a disproportionate stance, in OTL circumstances, we just would not be in Europe at all, save by invading and fighting our way to the Swedish borders via conquering Norway and Denmark and then having to fight off the British and in these circumstances, the French and West Germans and everyone else in western Europe. (Except maybe Francoist Spain I suppose, and whatever dictatorship we might have imposed in Greece, but we would not have access to the latter; perhaps we could bribe Italy to stay pro-Yankee, maybe).
They aren't going to stand aside and let Uncle Sam pick on a smaller power unhindered--whereas if they agree with Washington, soberly, that the Swedish regime, which would have to be ATL nasty, for much weightier reasons than expressing sympathy for the right of Vietnamese people to have different political opinions than dictated by the US security complex (which remember, not all US citizens agreed with, especially after the ongoing debacle in 'Nam) then in that case it would indeed have to be a bloc action, the risks, costs, guilt (and credit) shared by all the major NATO powers--and if we are not so ATL the USA is already out of Southeast Asia on our ear, it would in fact be the European forces that outnumber the Yankees. If the USA commands the same degree of respect it did OTL despite Nixon (or if you like, reservations about Johnson, Kennedy, and even Eisenhower (the Suez crisis would like a word with him after all)) then no doubt the US forces would be leading and coordinating the joint effort, but it would hardly be properly labeled "US invades Sweden" except I suppose in suitably slavish US newspapers and TV reports.
With all NATO in on it, the military situation is quite different of course--the main thing would be to contain the Swedish navy and air force in the Baltic while mustering a land invasion force in Norway then surging over that border to systematically secure the place. Which, again, if Sweden retains both its OTL military quality and quantity, and also general loyalty of Swedes to the regime, would be a hard and costly fight, one NATO would win by attrition primarily--very fast attrition to be sure. Then God knows what it would take to occupy and suitably reform Sweden itself, a lot would depend on just how and why Sweden went all pariah in the first place. "They've got to be protected, all their rights respected, until someone we like can be elected!" Hah, that might be forever. Or genocide of course.
Anyway it is pretty inconceivable that Sweden would wind up doing anything that would approach justifying such an extreme response, or even making it plausible very bad men could persuade a nation or five it was the expedient thing to do. It is less inconceivable to me that the USA might turn into such an overtly blowhard and impetuous monster of a military dictatorship, but if we did, we'd lose all soft power and not be welcome anywhere in Europe save a few outposts themselves of dubious decency and quite weak in themselves, and a united Europe could well insist we don't lodge ourselves even there in places like Spain.
We'd be invading Britain or Ireland or southern France first, you see. And not get anywhere near Sweden until a general nuclear Armageddon ensues mooting the whole mess.