Once the vaccine has become globally available say from June 2021 then:
To enter any foreign country you need a Covid-19 Certification, similar to yellow fever to avoid spreading from or importing to the disease.
I would say this is absolutely necessary to improve the take up of the vaccine there needs to be at least a 70% uptake. In fact, I would make it compulsory for any means of travel where identification is required.
They can scream all they like about freedumb[sic] and the constitution, but, those end at the US borders. No certificate no boarding the international flight/cruise ship/train etc. You could even promote it to them as “build a Covid Wall”, paper is cheaper than steel and concrete. Antivaxers can stay home, until they change their minds.
I am pretty sure that many countries will go down this route.
Build The Wall!