I'll take a stab at the 'no shirt, no shoes, no service' one.

https://www.findlaw.com/legalblogs/law-and-life/no-shirt-no-...

https://www.sporcle.com/blog/2019/12/where-did-no-shirt-no-s...

Second source there I haven't run down secondary facts on, so take it with a grain of salt.

However, the gist is, there is no health regulation mandating no shirt, no shoes, no service, people are totally free to attribute their policies to whoever they want, and for the most part, even if the sign is there, who says it's going to be enforced, and if it is, it's not violating any explicit/implicitly granted rights without relevant case law which I'm not digging into right now.

So that policy is more a matter of personal taste in operating a business, whose frequency evolved to a sort of cultural habit.

Masks/vaccines, unfortunately are a bit different due to the admittedly dicey history the entire policy sector known as "Public Health" has had in terms of what gets crammed under it's umbrella.

Examples:
The notorious mistreatment and abuse of mental patients in asylums:
Public Health

The Tuskegee Syphilis experiments:
Public Health

Surreptitious DNA collection by intelligence agencies from needles used to vaccinate people in Africa post 2001:
Subverted Public Health, but Public Health nevertheless

Eugenics:
Public Health

Adding compounds (gualfenisin) to medicines that have a "recreational use" (dextromorphan), and refusing to sell the unadulterated compound any longer?:
Public Health

Think about that last one. You're literally introducing a compound to a substance that poisons more readily to get those damn druggies to stop using it. This is not consistent with cultural understandings of the Hippocratic Oath, which when you're dealing with any sort of medicine or medical derived authority, is critical toward maintaining the necessary trust to even convince patients to let you help them.

When politics and medical science meet, you get Public Health, and it isn't necessarily the medical science that injects the mistrust, but the political hand that controls what science is put out for public review. Organizations have agendas, and the subtextual agenda can sometimes be enough to dissuade overall credibility in light of having "seen it all before".

The fact policymaking flip-flopped as much as it did, and the level of mere appearance of unethical behavior/conflict-of-interest, and loss of impartiality through systemic conflicts of interest between the private sector supplying the public sector with the tools they need to enact their policy justified by science funded by... the private sector... The room for skepticism in a micro-perspective of one person's life, is large enough to comfortably fit a few elephants.

I don't expect you to walk away from reading this with a sense of "Oh, that makes sense, that must be it let's fix that"... However, there is so, so much more to where the distrust and controversy comes from than "people just aren't being logically consistent". In fact, people not being so is the starting point for trying to do anything civically. The challenge is trying to get as much mobilized as you feasibly can. The trick comes in, in that you carry with you all the crimes of your policy making edifice past.

Atonement and trust building, as it turns out, is hard.

Make some sense at least? Or at least shine some light maybe?

P.S. This unintentionally veers into a research interest of mine which is the creation of "shadow laws" via the structuring of incentives by policymaking orgs whereby they create enough uncertainty to get organizations to make privately enforced policies to get something done now, without actually having to commit a rule or regulation to paper to have to get erased or repealed later.

This exploits the human characteristics of "anticipatory obedience", also known as "you get what I mean?" or "telling someone to do something without outright saying it" It isn't something most people talk about, but whenever I observe management or leadership types, I see it all over the place. I call it "hearing the unspoken parts."