... Except for some people, though, right?
I have an idea how you feel about the guy refusing to sell (decorate) the gay marriage cake (not trying to be pithy here, just tried to do a bit of footwork before replying). Do you absolve that guy under those "American values and traditions of free speech" as you would a website in this case? For me, second-order consequences are as important as whether or not this particular guy must sell this particular cake, when it comes to issues as critical to a functioning free and democratic society (such as speech). So "fair" abstractions (those which don't hide or ignore contradiction) aren't just important, but obligatory. This is an issue that can be reasoned to completion without introducing "protected classes" of human being, because the reasoning and conclusion are the same regardless (and for the same reason more concise mathematical proofs are preferred over those predicated on "complications" such as Riemann).
The guy selling the cake argued that he was being compelled to express an opinion (decorate a cake in celebration of an idea his religious beliefs dictated were unethical), thus making it compelled speech. So, is Youtube being compelled to express a particular opinion, if they do not ban users from the platform, when those users say things people find abhorrent? I do not think so, because Youtube bills itself as a platform where users create content and then publish the content on the platform for other users. Youtube does not purport to be a merchant of the content itself (obligatory reference to criticality of Section 230 protections). But according to his legal defense, the cake guy is selling the decoration of the cake in addition to the cake itself; his artwork as an expression of himself. In other words, Youtube is selling the medium and not the message. But the cake guy is selling the message (in addition to the medium). He is billing his cake decoration as part of his services, whereas Youtube and every other "platform" specifically denies in legal long-form that the content on their platform(s) reflect the views and opinions of the companies creating them. That is the critical distinction, and why I feel strongly that any platform which displays in its ToS that users agree that the views expressed on its platform are not the views held by the company, is violating the right of free expression to the users they ban from their platforms for the speech those users express on their platforms.
Importantly, a big part of my reasoning here is that, subscribing to stoic thought, I place accountability for any perceived "damage" from words on the shoulders of the person interpreting them. I mention this here because I've found this is so divergent from the dominant worldview that it's rejected often with much of the same forcefulness as if I'd stated a value judgment predicated on the color of a person's skin. And this seems to me to be symptomatic, and I'm not sure how this fits into the broader discussion of how the internet fits into our culture. But it's a core proposition which I hope will be addressed directly instead of indirectly, because the implications are clear (you are ceding control of your mind to others, when you allow their words to dictate your thoughts).