You're missing the concept. Which is many people believed them without question because the government said X and scientist proved Y, etc... And Germany is a well educated country, not a 3rd world shit hole. Same went with the segregation of blacks here starting in the 30's. Tuskegee airmen were told by PHD scientist that blacks can't see at night at the senate hearing whether they should be able to continue to fly or not. So not the same as the holocaust, but same concepts.
So is it proper to segregate someone just because of a choice that they make? Is it OK to restrict their freedom without trial because of a choice they made. Is it OK to close businesses and stop people from earning an income because of vaxx status. These are rhetorical and again I'm referring the the concepts that the questions ask. Because I'm sure there are some examples where yes you can is the answer. But generally speaking is what I'm getting at.
The reason like race, vaxx, religion is only a small part of the machine of evil.
I have noticed that many people always seem to rush to the worst assumption about their opponents (political, sports team, country, etc) and there is no difference here. Instead of looking at people who want vaccine mandates and saying "I can see how they think mandates will solve the problem but I don't agree with forced injections" so many go straight to comparisons with Nazi Germany and the holocaust. I can see how it serves a certain function in situations like for the military in wartime (easier to kill someone demonized than humanized) but it isn't a tendency I have by nature so I don't understand this tendency, I don't go straight to the worse comparisons.
As to your question about whether its OK to close businesses and fire people because of their vaccine status, some people certainly seem to think that is acceptable but I don't think they are looking to wipe out a group of people (you don't wipe people out by giving them medicine to save them). They don't wish for anyone to be segregated, they would rather everyone be vaccinated whereas the Nazi's didn't just want Jews to become patriotic Germans. Their intentions are much more reasonable and rational, they believe that if everyone gets vaccinated they can save more lives and we can go back to normal life sooner. They think that people who are refusing vaccinations are holding it up for everyone else and thereby harming everyone else. They then conclude that this is reason enough to strongly incentivize people getting the vaccine. Personally I somewhat agree with their logic but not with their conclusion. The fate of the entire country could hinge on whether a person took a vaccine and I don't think I would ever condone the government forcing that person to take it.
The current evidence does show that our vaccination status affects other around us so it is undeniable that our vaccination choice affects our neighbors, it isn't merely a personal choice with no repercussions. Now the data also shows that a vaccinated person has a greatly reduced chance of becoming seriously ill from covid (10 fold I think) so an unvaccinated person being exposed to a vaccinated person clearly isn't the death sentence some have made it out to be but the danger isn't zero either. Because of that, there is logic that supports the reasoning behind those who want forced vaccinations but I would argue the fear level is disproportionate to the actual risk. Regardless their "segregation" is one out of risk mitigation not a hatred for who individuals are.
One question you posed makes me wonder, when else might we accept segregation. I am not sure of any perfect examples but I can think of some similar ones. Sex offenders usually have to register and a website lists their name, address, and photo. Why? Because we as a society think they pose a risk to the rest of society, so we segregate them in a sense and place restrictions on them. In Hawaii over a hundred years ago patients with Leprosy were segregated to a certain isolated community because of the risk of spreading Leprosy (though people don't choose Leprosy). I remember a news story about a restaurant that had a sign posted saying Biden voters couldn't dine there. I think if I had was sick with symptoms of ebola you might want me segregated if I refused to seek treatment. I could go on thinking of more examples but I will just say that there are some times where I think we as a society do believe it is acceptable to restrict people's freedom from a choice they have made. The difficult thing is where to draw the line of when it is acceptable vs unacceptable
I think there is something fundamentally different from segregation due to risk mitigation and segregation due to hating a group of people for who they are. I don't think the Nazi's were simply mitigating a risk by trying to wipe out Jews. Flapp, I hope this reply hits some of the points to raise too.