In the 1970s the US required MMR shots for attendance in public schools and the disease quickly tapered off - we've done this before and, so long as the vaccinations aren't inducing a financial burden on individuals that are unable to afford it - I see no issue with requiring vaccination if you want to share a close space with others. A lot of potential partners will reject you if you're unable to provide negative STD results - this isn't all that different.
Oh also - a small pedantic correction. There is a formal thing in the US called the No Fly List and I've heard absolutely nothing about putting people onto it for not getting vaccinated - there has been discussion to restrict your ability to fly if you're unvaccinated though which... would be easy to fix (unlike getting off the No Fly List) by simply getting the shot.
First, public schools are government institutions, airlines are not. Sure, flight is heavily regulated, but do you want to live in a world where private companies form a cartel and all agree to require a medical treatment, effectively blocking you from long distance travel?
Second, their are religious exemptions to mandatory vaccinations. We can argue whether there should be, whether they're abused and all that, but as long as they're going to exist, shouldn't they apply across the board?
To the first point - yes because it's being done for a completely valid medical reason. There isn't a slippery slope argument available here because people consider this reasonable because the cause is reasonable.
To the second point - I think religion does a lot of harm to modern society so I'd rather those all went away - yes even for the amish as inoffensive as they are.
Oh also - a small pedantic correction. There is a formal thing in the US called the No Fly List and I've heard absolutely nothing about putting people onto it for not getting vaccinated - there has been discussion to restrict your ability to fly if you're unvaccinated though which... would be easy to fix (unlike getting off the No Fly List) by simply getting the shot.