This is an uncontested point: health officials can close businesses for any number of properly legislated reasons. A restaurant can be closed for unsanitary conditions, any building can be closed if it is deemed unsafe due to flaws in construction, maintenance, etc. Companies are legally shuttered when they engage in criminal conduct, go bankrupt, etc. -- all legally mandated under agreed-upon and well litigated/defended legal code.
There is no freedom without consequences, and in the case of public health, the remedy is closure, penalties, and quarantines that can land a violator in jail. So I answer "depends". So the best versions of what we call the lockdowns don't put chains over the doors (pre-emption), they say proscriptively "at this point in time, there are extra regulations in force for the public good, and you can and will be held civilly liable and punishable if you violate them." Governors, mayors, and public health officials have reasonably-wide discretion to set those limits, but not ENACT them. The difference is small but significant. Some places are getting the balance right; some are screwing it up terribly. Same thing for some groups.
So here's the deal: those codes and powers do not implicitly allow for non-legislative bodies such as in the federal, judiciary, state, or municipalities to contravene a group's constitutionally and legislatively written civil rights on a pre-emptive, selective basis. My best examples would be a bar or restaurant -- can be cited and penalized for violating even temporary rulings, and in the case of preventing public disease spread, those who have been to that bar or restaurant can be legally quarantined. A building deemed unsafe can be shuttered. The same thing about penalties, etc. applies to church gatherings, religious events such as weddings, etc.... once violations have taken place. Where I go to worship, the building capacity is around 1500 people; in the main meeting space probably 900. With six foot spacing, that might equate to 300 people in the building for any services. But it would be difficult if not impossible to maintain spacing, mask use, etc. in all of the building's classrooms, facilities, etc. -- so our local leaders agreed to suspend worship meetings on a voluntary basis in order to follow those guidelines. Ergo they do not risk penalties and the municipality avoids a First Amendment lawsuit and bad press. Melting pot & compromise -- an American solution that works for all our good because of choice, not by compulsion.
Contrast that with either targeted extreme orders which the Supreme Court has now rejected, or for businesses and other profit-oriented entities and/or religious congregations who deliberately flout the temporary regulations but demand exemption from the legal consequence as "necessary to maintain their civil rights."
Ergo: Depends. What think y'all?