This could be a problem, but I think it's manageable. There are some people who subscribe to pseudoscientific beliefs and or conspiracy theories regarding vaccines and others who simply deny that Covid exists at all or if they concede its existence, they claim it is being overblown and that the reports of mass infections and deaths are false. Happily those subscribing to these delusional views are not huge in numbers. But there are enough that in some situations they could pose a serious health risk if you get a bunch of unvaccinated people in large groups.
On the one hand I dislike direct coercion in matters of conscience. So I would be opposed to laws mandating vaccination under pain of fine or jail. But on the other hand it is a well established principle of law that society does have the right to impose reasonable regulations to protect the public health. So my response would be to take steps to limit the ability of vaccine resisters to pose such a threat.
* Require all persons booking commercial airplane flights anywhere in the US, or overseas if bound for the US, to affirm under penalty of perjury that all those booking have been vaccinated. No vaccination... no plane trip.
* Ditto interstate bus and train tickets and all cruise ships/ocean liners.
* Require affirmation of vaccination as a condition for applying for or renewing a US passport.
* Hotels should be encouraged to require registering guests to affirm that they have been vaccinated.
* States should require students registering for schools and university to provide evidence of vaccination.
None of these measures are unreasonable as a public health response to a dangerous pandemic. People will still be able to refuse vaccination, but there will be consequences that for many will be inconvenient. They could still travel by private vehicle and children could be home schooled. Obviously, any such regulations should not be imposed until a vaccine has been available to the general public for a sufficient amount of time that anyone wanting one will have had the opportunity to get the jab.