What would actually happen if a year or two from now, it turned out that, however unlikely it may appear now, there really were serious long-term vaccine side-effects?

There's absolutely no way it would involve the pro-vax people saying, "We're sorry, you were right." More likely, the same political sides would dig in further, there would be a bunch of attempts to cover up and revise history, and the message would be "The evidence has changed, but people who never got the vaccines didn't believe in science and were still selfish and wrong."

That wouldn't be true if this were really about health.