Well, mass hysteria is a real thing, but if a large group of people who have no prior reason to cooperate all claim the same unusual observations, it's certainly much stronger evidence that something unusual was going on than one individual making such claims.

Many, possibly even all religions though, make claims of supernatural events being witnessed by large numbers of people, and religions make enough mutually exclusive claims that they cannot all be true, so we know that claims of large scale supernatural observations are something that must at least sometimes arise in religions that are false.

In terms of the falsifiability of religion, it's important to remember that we're essentially working with a stacked deck. In a world with one globally accepted religion, with a god that made frequent physical appearances, answered prayers for unlikely things with sufficient regularity that we had no more need to question whether prayer works than whether cars work, gave verifiable answers to things that humans could not be expected to know without its help, and gave an account of the provenance of the world which was corroborated by the physical record, then obviously the prior for any claims of miraculous events being the result of genuine supernatural intervention would be completely different than in our own.

If a pilgrim child in America in 1623 claimed to have spoken to a person from China when nobody else was around, the adults in their community would probably conclude that they were lying, confused or deluded in some way, unless presented with a huge preponderance of evidence that the child would be highly unlikely to be able to produce, and it's completely reasonable that they would behave this way, whereas today, an American child claiming to have spoken to a person from China demands a very low burden of evidence.

In a world where the primary evidence offered in favor of religion is subjective experiences which have a pronounced tendency to be at odds with each other (people of different religions have experiences with mutually incompatible implications,) if a person who claims highly compelling religious experiences is unable to persuade other people, it does not indicate a failing in the other people's rationality.