Masks do something VERY beneficial -- just not the thing being claimed.
Don't think about masks like an engineer, but like a psychologist. Masks reduce anxiety. They're a magic talisman to keep the demons away, a rain dance to end the drought, but with enough cargo-cult science vibes to be superficially convincing to secular moderns.
Mask also enable cheap status-seeking: with masks, they're very smart people following the science, and heroes protecting the community, and they get to sneer at their "selfish" inferiors, all without having to make any real effort or sacrifice. (Since masks have become a "blue" tribal marker, there's an assertion of group superiority as well.) And frankly, a lot of mask fanatics don't seem to have much else they can leverage for social status.
When we point out that masks don't actually work -- including tacitly, by not wearing them ourselves -- we're taking that away from them. You can see why that would be upsetting to them. How to break that spell, I don't know: the more you show it's true, the more upsetting it is, and the more fanatically it must be rejected.
Still, challenging them may at least stop others from falling under it. And challenging them annoys them, which is all to the good.