Luke, I can barely handle the bitcoin/anarchy stuff. :-P
The solution to your question is what I already stated: The scientific method. Science regularly said "well, that was wrong, gotta rethink this." That's what makes it so reliable, and made it able to usher in the greatest advancements in human knowledge since ever. Making a change is not always easy; it requires evidence, data, and a good logical argument. But in time, those win out.
But if someone still thinks the moon landing was faked? Or that the global climate isn't getting warmer? Or that vaccines cause autism? That's just deliberate ignorance of the facts, and no, you don't get "alternative facts."
When considering alternate opinions or perspectives, which you can and should do, you should always evaluate them rationally. If they fail a rationality test, then... no, I am not going to stay open to them.
I have never seen X-rays myself, but I have seen ample evidence that they exist, and have trust that the institutions and people that study them are, overall, honest about their findings. (The best way to evaluate someone's honesty: What happens when they're actually wrong. Do they own up to it or try to cover it up? If they own up to it, I am more willing to accept their word for it the rest of the time.) If the current understanding of electromagnetism was way off, we would physically not be able to have this conversation. Are there gaps and details that we don't understand or may have wrong? Absolutely, and science freely acknowledges that. But "there is no such thing as ultra-violet light" is... no, not actually a thing.
An alternate epistemology has to justify itself rationally. If it can't, then no, I am not going to accept it.