>Is that similar to the k-12 "mandate"?
Yes. In the US, you largely can't attend k-12 (remote or not) without proof of all your vaccinations either. Ironically, those required vaccines don't include COVID yet. Many jobs also require proof of non-covid vaccinations. If you aren't vaccinated for something, you put those around you at a higher risk for it -- even if they are vaccinated. COVID isn't a special case here.
Any time you have a contagious outbreak of anything (for example, outbreaks of any of the many other things we require the general public to vaccinate against) you see very similar measures taken to contain and eradicate it: isolating & controlling an area's ingress/egress, required quarantines, mandated vaccinations (when they're available) and/or widespread, repeated negative tests and a reduction in spread before returning to a "status quo".
This vaccine (and other infectious control methods) are an existing, by-the-book response to an epidemic-turned-pandemic disturbing the status quo. The Supreme Court ruled [1] way back in 1905 that it was lawful to punish and "infringe upon personal freedoms" of those who refuse a vaccination during a public health crisis. This is nothing new.
B.1.351 (Beta) and P.1 (Gamma) and several other variants also reduced vaccine effectiveness, but vaccinations proved still more effective than not being unvaccinated. The possibility for a mutation that completely avoids a vaccinated body's preparatory methods has always been a concern -- however, 1) no variant so far has come even remotely close, and 2) that's exactly why everyone needs to get vaccinated: to cut down on spread and, therefore, potential mutations (and ultimately, of course, to contain the outbreak and get back to a relatively normal status quo).
I'd love to see whatever "reports" you're referring to about those with the vaccine having a lesser ability to respond as those without it. That's something I haven't seen, nor am I seeing anything from a few searches online or in recent publications, nor does that really even make sense with how vaccines as a concept (or in real-world applications) have worked for centuries.
https://www.cdc.gov/nchs/fastats/immunize.htm
This shows that a very high percentages of children are vaccinated by the time they are 2 years old (e.g., 90% for MMR). Too me, this strongly indicates that those policies aren't very porous at all.
Are the covid vaccine mandates any less porous, especially given that only about 60 to 70% of adults are vaccinated, even though pretty much all adults could be vaccinated by now.
The old vaccines were new at some point too, and I would wager that development and testing regimes weren't as robust as they are now. I don't see any good reason to trust the new vaccines any less.
Finally, I didn't say the policies are equivalent in every way, but I still contend that they are fundamentally similar with regard to mandates.
So weird that folks seem to think these things are at all equivalent.
In New Zealand you will not be able to work (remote or not) if you don't get the vaccine.
Is that similar to the k-12 "mandate"?