I mean... does Youtube have any obligation to host any content?
I believe it's pretty clear that they can (and they do) take down any videos they don't wanna host, regardless of the reason.
That's the crux of it, and the answer is no. They still need to obey civil rights laws. They couldn't, for instance, ban women from uploading, or Asians, or any other protected group.
Sure but that's a different topic. We are talking about the content they host, it's the content what they can take down for any reason. Of course they can't ban an individual based on one of the conditions that are protected by human rights, but they can ban them based on what kind of content that person posts. He wasn't banned because of being an antivaxer (even if that isn't protected), but because of the antivax content he posted. Even an antivaxer can post content in Youtube, as long as it's content Youtube is ok with (eg. not antivax). I'm sure there's a lot of people with controversial ideas that happen to post content within the limits of what Youtube tolerates.
Youtube often takes down content that shows too much of women boobs, but they are ok with showing men boobs, for example.
You can't refuse selling a calendar to a woman (for the reason of her being a woman), but you can refuse to sell calendars that have pictures of women on them if you decided that's not what you wanna sell (and you don't even need to justify it). For example.