I believe some people in this thread still have a simplistic, Cold War-esque view of politics and just using a single spectrum of left-right leads to mistakes.
For example Nazis were extremely heavy on statism and regulation but also right wing as
culturally. Who is more right wing, a Nazi or an Anarcho-capitalist? it depends: do you mean right wing in the cultural sense of wanting to protect tradition, your nation, and other conservative values? Then the Nazis, or do you mean "right wing" in the economic sense of wanting to protect free market capitalism from state meddling in whatever way? Then the Anarcho-capitalists. Either way commies are going to hate you.
You shouldn't analyze political views on a single spectrum or you'll fall into these kinds of problems.
IMO the easiest and minimum tool to use seriously is the two axis political compass with conservative-progressive and liberty-statism (I prefer to have 3 axis with freedom, culture and economic equality but whatever).
In the two axis political compass Nazis are very conservative and very statist, socialists are very progressive and very statist, anarcho-communists are very pro liberty and very progressive, etc.
Most people however are not in the extremes of those two spectrums but somewhere in the middle. Personally I'm more conservative-leaning and I rather value individual and market freedom but I believe the state can and should intervene in certain situations in the name of public good.
Back to this case, if this had happened in 2006 I would be completely against the idea of forcing Youtube to accept people it does not want in its platform because not only did they have a ton of competition from similar pages but they weren't as relevant when considering media as a whole. It would have been unnecessary and therefore unjust to limit their freedom of enterprise.
Fast forward to 2019 and its a whole different picture, YT not only rules internet video market but is giant for media as a whole, especially when you consider younger people. However the most dangerous situation is that the same happens with most social media sites where a handful companies control everything and if you get simultaneously banned form Youtube, Facebbok and Twitter you are an internet media corpse as I said earlier. Personally I'm not that far in the freedom spectrum to be comfortable with handling corporations such power to control information channels and discourse and I believe you have reasonable arguments to defend the idea that the state can regulate them in the name of freedom of speech, plurality of ideas and to curtail potentially dangerous oligpoloistic corporate power in general.