Of course, if people are just blatantly ignoring or refuting established scientific results, there’s not much you can do…
Well... there you are, unfortunately. That will happen pretty much literally every time, no matter what you do, because it was never about the science. It will never be about the science, because we already know they're completely wrong about everything and therefore they need to make science irrelevant.
Conspiracy theories sell people the idea that they're seeing through "the bullshit" (sum total of human expertise, generally) which is a powerful feeling, that the dull world of undeniable facts and logic can't quite measure up to. Too easy to deny them anyway, you see. The package tends to come with a bunch of rationalizations for why, the instant you seem like you're not buying it, they no longer have to listen to anything you say.
Acknowledging that plenty of common vaccines have extremely rare, but nonetheless potentially severe side effects.
Unfortunately, if you don't also want to acknowledge the ones that are blatant lies, you are instantly The Enemy. Given stuff like belief perseverance and the backlash effect it's understandable to want to try, though.
Being "supportive" when arguing against known bullshit is not my forte, so I wouldn't be the one to get good results out of the supposed strat of... agreeing them out of their position(?), but I am damn curious about what it'd look like.
To me personally, the choice is easy (I press the button), but I recognise that people see this as a dilemma.
A false one, to belabor the point, but it's not relevant anyway. The reality is that if you get within light years of the concrete thought experiment, they'll be real suspicious. If any part of it is remotely realistic, you'll lose them instantly: "do you want a thousand times higher risk of death, and also help spread a potentially lethal and disfiguring infection?" cannot be made to sound all that reasonable.