First off, 50% of the country believes things that actually have no evidence other than people they like saying it. It's not about different truths, it's about truth and fiction. All you need to do is try and verify claims from first or second hand sources, and that becomes painfully obvious, but people refuse to accept that or be open to it.

Second, nobody is asking to have a partisan arbiter of truth. The supreme court was once non partisan, and they're an arbiter of justice. Even conservatives who are actually capable of researching and following truths come to the same conclusions as the left when it comes to facts. Here's an easy one: Conservatives all over the country claim there was evidence of election fraud. Okay, it's been years, where is the evidence? No where, they didn't even fabricate evidence, they literally didn't submit anything. Any rational person, regardless of their political views, would agree that there is no reason to believe the election was stolen. Trump is going to trial for espionage. Where is the evidence? You can literally listen to some of it on the internet, there are photos, a large investigation with multiple people on both sides of the aisle took place, there were raids and testimony. But there are still people claiming it's a witch hunt and there's no evidence.

It's not even censorship if they just mark things as not true. There's really no reason doing something about it has to be equivalent to full scale authoritarian censorship, so you're walling yourself off from actual solutions with a slippery slope argument that leaves us in the hands of disinformation campaigns, which are easily paid for by rich people and foreign governments.