My wife is very vaccine hesitant, and every time they make a move like this to block content or take it down, it only strengthens her position. She thinks they’re taking it down because they don’t want people to know the truth. The only thing worse than bad ideas is the suppression of bad ideas. It’s tragic that we knew this at some point, but are going to have to figure it all back out again the hard way.
One of my family members is also very hesitant to get the vaccine and gets all kind of anti-vaccine propaganda through various groups and channels. She takes that content as "reasonable" and "potentially true" even tho basically all of what I've seen is simply untrue. E.g. an article claiming there were more deaths due to covid vaccines than to covid, which is "backed up" by official NHS statistics. How did they arrive at this claim? Well they just said any recorded covid death with a recorded precondition didn't die due to covid but due to the precondition and any death that occured within 14 days after a vaccine shot was definitely because of the vaccine. I think I don't have to explain the logical fallacy in that argument, but it does make for a nice headline and many (most?) readers only read the headline. Who really takes the time to carefully read and see if the claim has any logical basis? To make things worse, this kind of "news" is regularly republished across multiple sites hiding the "data" multiple links deep (if directly linked to at all).
That's the kind of content many anti-vaxxers are exposed to on a daily basis. For your line of reasoning to make any impact it would mean that not blocking this kind of content actually weakens the positions of anti-vaxxers. However, I strongly belief the opposite is the case. Being exposed to this kind of content and treating it with similar credibility as other news/media is strengthening their position too.
So we have a situation where keeping the content is reinforcing the beliefs and where blocking the content is also reinforcing the beliefs, because "legitimate" content telling "the truth" is blocked "without reason".
I'm also not convinced that outright blocking it is the right move. Hindering it's discoverability (e.g. by downranking it in the so dangerous social media reinforcement bubble algorithmns) and somehow making clear that it might be of very low credibility might be a better approach. It might also be equally hopeless.