I'm sort of sympathetic to that argument except:
1. I think at the end of the day, the problem isn't "does YouTube have the right to do this?" it's "should YouTube be doing this, given their status?" For me even though they have the right to, I think it's just the wrong thing to do.
I personally am baffled by how the US as a society seems to be devaluing free speech principles in the private and public sphere due to some argument that it's needed to combat misinformation. This strategy never ends well, and it belies a lack of strength in promoting alternatives. The way to combat misinformation is with better information. Resorting to free speech restrictions is a sign of weakness in my opinion.
In the end I'd rather have YouTube (and other platforms) modeling a different approach.
2. I also think, regardless of how they got there, at some point a private business functions as a monopoly and should be treated as such. I'm not so sure how I feel about regulations along those lines, but I do think anti-monopoly legal response to this sort of behavior wouldn't be unreasonable. I'm not at all sympathetic to the GOP in general, but if they started coming down on YouTube for this kind of thing under anti-monopoly regulation umbrellas I think it wouldn't be irrational or unreasonable to me.
3. As a more immediate issue, I think this sort of thing always backfires. If you have a bunch of people thinking there's a conspiracy to shove untested vaccines down people's throats, and then you have a major media distributor like YouTube censoring all anti-vaccine discussion, what do you think they're going to conclude? I'm as pro-vaccine as someone can get, and think arguments against them are usually pretty absurd, but I have to say that this kind of thing starts to look like a conspiracy, even if it isn't one. Why give them ammunition? If you can't convince people the vaccine is a good thing, how do you think that shutting down discussion is somehow going to work better?