Whenever one feels like they are between a rock and a hard place, they should stop and ask "How did that hard place get so hard, and is there something we could do about that?" The only reason there is a dilemma in your imagined (?) scenario is because people are not educated. But understanding that fact doesn't do us any good in the instant case. It's too late now to send everyone back to school to teach them science, calculation of odds, relative threat assessment, etc.

So, what to do?

If we don't tell them and word gets out, then it just provides more ammo to the anti-vaxers. If we do tell them, the unenlightened self-interested might keep us out of herd immunity.

I think the answer is to tell them the truth and then do what some jurisdictions are doing: Appeal to the self-interest by paying people to get vaccinated, hold lotteries, give beers, have hot chicks or dudes administer the vax in their underwear.

Dummies will gladly drive tons of Detroit steel, hurtling down a highway at 70 miles per hour, mere feet from a thousand others doing the same thing, some going the opposite direction, risking their lives because Power Ball is up and they want a ticket. Or to get to the strip club, or to work in a cubicle for the man. Whatever. So they will gladly take a vaccine, especially when they don't personally know anyone who ever died from it. People are stupid so all you have to do is use that for them.

Then think, "How can we avoid this in the future. Oh yeah! School!"