Maybe the comparison with amputation is a little over-the-top but let me illustrate with a few other real-world examples why this kind of concern is not completely illegitimate.

The health policy in some countries e.g. in France (and maybe large parts of Europe?) actually allow you to have an "health passport" just because you recovered from Covid recently enough.

It would actually be illegal in France to privately require proof of vaccination if not exceptionally allowed by a narrow law (as a general principle, medical information are very protected here).

Some Covid vaccines have been forbidden for people under a specific age limit, although they were allowed for a while, but the risk has eventually been reassessed after a few suspects side effects (very very rare, but considered a risk important enough to change the policy, esp since the risk of covid itself decrease greatly the younger you are, and there are arguably safer alternatives in other models of vaccines).

Of course it is still probably "on average" better to get vaccinated on top of recovering from Covid, and of course the comparison with amputation was probably over-the-top (at the very least it should have been stated as a risk of "amputation" with a very very low proba); but overly constraining people is debatable -- especially when tons of factor are hard to be synthetized to "everybody should just get vaccinated right now, unconditionally, -- and accept to be privately controlled by anybody -- or they are horrible antivax people and people will die because of them"; not everybody has the same amount of social contacts with the same categories of people and/or live in the same kind of city and accommodations, public health is not something that appears in empty social contexts just because of raw numbers and models, etc.

Yes it probably would be better if "everybody" was vaccinated. Willingly. And if we had decades of feedback to convince people. And if they were vaccinated against other diseases too. Now welcome to the real world and think of how to navigate efficiently with imperfect knowledge, including how to avoid entirely dismissing concerns.

Primum non nocere certainly does not to be dropped and hopefully will not: the situation is shitty but will become clearer with time, and if we detect either more risks or more safety for various vaccines hopefully the policies will evolve accordingly, and individual opinions too. Note that they already are not completely binary and that it is still kind of hard to decide from which age we should allow / incite / require vaccination -- and the "optimal" solution probably depends on the coverage of the rest of the population too.

And that's because of that very principle. There is no exact obvious point where all-in starts to be required. It maybe would be useful to make regular-flu shots more or less mandatory (and now even the interest of flu-shots is debated by serious scientists because it may be counter productive for the state of the immune system latter in life; or that may depend on people -- maybe new strains of covid would yield to similar debates in a few years?). They are typically not.

That being said my current understanding make me wish more people go get vaccinated, but just do not pretend it is all black & white and that people should not have subtle/reserved opinions.