They won't care - it's for foreigners only.
Just like them fingerprinting all non-citizens entering the country, if they did it to locals all H#ll would break loose and there would be lawsuits flying left and right...
You are probably right.
However I think a large number of countries will follow the the Lead of the USA, and require visitors be vaccinated (and perhaps go further and require their own citizens be vaccinated for isolation free arrivals). The USA is significant enough globally that it placing this rule will mean that other countries will feel comfortable to do similar...
I suspect in a years time the international (isolation free) travel options to un-vaccinated people is going to be pritty limited, and those that do allow it may well require additional PCR tests at the travelers cost.
What is going to be interesting is the detail.
Will vaccination certificates from all countries be accepted (even those with high fraud rates)?
Will all vaccines be accepted? Just western vaccines? Just WHO approved vaccines? Notably Sputnik 5 is not WHO approved despite being pritty good. China for a while would only accept Sinovac and Sinopharm vaccines.
Will better vaccines (i.e. pfizer) be treated the same as less effective vaccines (i.e. J+J)?
Will the vaccines need to be given in the past 12 months or boosted?
Will mix and match vaccine doses be accepted?
Tempting for countries to insist on only the best vaccines for entry, but this is pritty harmfull from a global perspective if we have people getting re-vaccinated with other brands to meet travel requirements when the third world is still crying out for their first round of vaccines.