I'd start by having Twitter, Facebook, etc. flag content that has factually untrue material and show content that has the facts or refutes the false content. The way to overcome disinformation is with correct information. It'll never be 100% effective, but it's far better than doing nothing and IMO is much less ripe for abuse than censorship.
Another tactic is to demonetize or otherwise remove the financial incentive of disinformation. YouTube has been doing this to mixed response thus far. This isn't censorship in that it does not prevent the information from getting out, but it does remove the incentive for sources to lie in order to make money.
A lot of the issue with disinformation is not just that it exists, but that it's being pushed by coordinated efforts. A way to combat this is to take a hard stance against bots and people having multiple accounts on sites like Twitter and Facebook. It's not an easy problem to solve but suspending or banning people (or IP addresses) when bots or multiple accounts are detected is another deterrent.
It's not at all in the same realm as book burning, but it is censorship whether you like the connotations or not. And to be clear, I'm not saying all censorship is bad. For example, exceptions to the 1st Amendment like yelling "fire" in a crowded place or inciting violence are not protected speech and can be censored by the government.
As in many things that are complex interactions among people, there's no way to prove that my view is better in all cases. But also means that you can't prove that censorship will be better in all case either. It's a gray area that requires debate and consideration.
But it's not just me that has that opinion:
https://reason.com/2019/05/13/fake-news-is-a-really-dangerous-excuse-for-censorship/
Look into the Streissand Effect for why censorship can be counter-productive. For example, the current NY Post nonsense was barely a story until Twitter banned links to it.
Here's a good deep dive into the current state of disinformation by the conservative Brookings Institute including a bunch of ways to deal with disinformation:
https://www.brookings.edu/research/how-to-combat-fake-news-and-disinformation/
I agree. "Who watches the watchers" is perhaps the most important aspect of any system with checks and balances.