We can thank the Slaughterhouse Cases for the disaster that is legal precedent in this area; the idea that a citizen's privileges and immunities don't limit the police powers of a state is ridiculous. This would almost certainly apply to localities as well (see the fact that they can't violate civil rights protections.)

And yet, Justice Thomas is the lone voice in using this clause correctly, while the others largely prefer to leave it in its neutered state and distort the equal protection clause to fill gaps where necessary and create some bogus guarantee of fairness. See Timbs v. Indiana for an example of just how ridiculous this particular area has gotten. There is some hope that Gorsuch may come around to Thomas' view, as he wrote a similar concurrence.

It is certainly a privilege of a citizen of the United States to run his business as normal. Police powers cannot overrule that. I fear that the precedent has already been set, however. The court system is too slow to work these things out while they're happening, and a ruling against an action is little solace once it's already happened. There must be significant punitive action against any state or municipality that attempts to do so.

I'd like to see Dillon's Rule states threaten to dissolve and re-constitute any municipal government that instituted any lockdown order at all. It would also nice to see criminal prosecution of those who threatened citizens who simply wished to go about their lives in violation of the constitution. A government official who does something of that sort without authority is acting as an autocratic thug and any physical enforcement of such directives is assault and must be prosecuted as such.