There's plenty of precedent to requiring vaccinations, especially in schools. And the US government has already stated that employers requiring a vaccination in this case is generally OK.
A number of African countries require proof of yellow fever vaccination to enter. The vaccine certificate is issued by each country but conforms to a WHO standard.
Most employers are reasonable and don't make you do dumb things like wear full PPE for a job that really doesn't deserve it in a poorly ventilated space on the hottest day of the year and other common sense things like that.
However, the kind of people who do safety for unreasonable employers (usually process driven BigCos, mines and shipyards are good examples) and the kinds of people who's only exposure to industrial environments is the mandatory safety training they took once upon a time for their internship tend to dominate internet discussions about PPE and safety. This results in some real gems of insanity.
Having worked in an enormous heavy manufacturing facility at a company with a very good safety record, I disagree. In the case of working on the hottest days of the year in full PPE, additional mandatory breaks and hydration are required. Additional airflow should be added if in a poorly ventilated space and compatible with the work being done. PPE used should match the risks presented, which should be well documented before starting work. Shortcuts to the standard process, failure to identify when things start going wrong, etc. cause injuries and deaths.
Safety culture is super hard to build, taking years of collaboration between management, workers, and unions if applicable. Every group wants nothing more than for the employees to go home the same way they went to work.
Any one time you do a task with less than required PPE, probably nothing will happen. But over the course of a career, those "this one time" instances add up and eventually will cause an injury or death.
Seems like a pretty easy distinction to me.