Something like the notion of a DMCA shield; where a platform can expose third-party content without consequences so long as they response to take-down requests means that they do not get to do filtering. If they get to do filtering and curation, then they are also directly responsible for copyright violations or libelous use of their platform -- the shield shouldn't apply unless it cuts both ways.
That is, by accepting some immunity from the consequences of free speech, they are then subject to free speech restrictions on their enforcement of their own opinions. A newspaper, for example, is not subject to the same restriction -- they are responsible for all content they publish, so can choose to publish or not publish whatever they want.
This isn't a precise framing, but I'm trying to capture some of my general thoughts on why I find it unappealing that YouTube and Facebook can filter out content that they deem offensive.
Facebook has a natural filtering mechanism through the ability for a user to restrict what they see. If you find content offensive, unfriend or block the person and you're done. Youtube can exercise some discretion in auto-play and recommendations, but they shouldn't be able to ban content unless they are required to do so by inheriting legal requirements.