If people are going to classify YouTube as a public square, does this apply to all forms of social media then?
Depends. Do free speech laws and protections apply to
all kinds of gatherings, speech, etc.? There will always be exceptions, but in the main I think that the social media companies like YouTube, Facebook, etc. should get at least the same level of treatment as the Christian baker who may be forced to serve someone whose views or actions he or she finds odious. In those cases, the bakeries (and floral shops, etc.) lost their cases on account of their being "public accommodations", so I guess the question should be: do social media companies serve the public or do they not? I could see the argument being made in the early days of Facebook, when it really was by design restricted to college students, that it does not amount to a public accommodation, but today now that anyone and everyone can join (fictional characters have their own profile) and largely has, that argument would no longer hold. Ditto with YouTube: it may have originally been designed to be more private than it currently is, but now that it is completely public, I do not see the compelling interest that speech be silenced beyond that which is absolutely necessary to comply with state and federal law (and NOT the blasphemy laws of nations like Pakistan, which banned YT for three years ending in 2016 or so due to its hosting of 'blasphemous' ex-Muslim/anti-Islam/doubting Islam videos).
Perhaps you see things differently, but I don't see this as a particularly 'conservative' vs. 'liberal' issue. It's more of a "can we please decide what to do about the reality of our social world today" question, which I don't trust the companies themselves to do without the oversight of the people -- not just the people they've hired to perform this very work, but the people that monitor free speech online, too, like the
Electronic Frontiers Foundation and the
ACLU. There should be, as in all things, a balance of the concerns for free speech and matters of safety and justice that errs on the side of free speech, as is supposed to be the American ideal according to pretty much everyone. I.e., I doubt anyone of any political stripe would be for losing
their own freedom of speech, even though this means tolerating the speech -- not necessarily the actions, and certainly never the
criminal actions -- of others. This used to be the grand compromise that made society function, and I agree that some really are pushing it, but that's kinda what any society is, y'know? And YouTube and all these other companies are a part of that.
TL;DR: Yes, if they can be reasonably classified as "public accommodations", which I believe many of them can be.