1. There are a small but very loud minority of people on the far left who are authoritarian and want to suppress all speech that they don't like (there are such people on the far right but they are much less politically influential than they were a couple decades ago). At this moment in time, far left authoritarians are trying to ban dissent from their preferred points of view via claims of "hate speech" and "disinformation". The first amendment was designed precisely to protect unpopular opinions, even odious ones, and there is no requirement in the first amendment for truthfulness.
2. Speech has moved online, increasingly to a very small number of social media platforms and mass media that is controlled by a very small number of owners. This provides a very small number of choke points where an enterprising authoritarian, either private citizen or government actor, can suppress speech that they dislike. The "algorithms" argument is a red herring; the most basic algorithm is "publishers I choose to follow, in reverse chronological order, and excluding publishers that I block", but the social media companies can't resist making it more complex and not providing this basic capability as a selectable option.
The solution to #1 is to fix #2.
The solution to #2 is to end corporatism; let's stop treating companies exactly the same as we treat humans wrt rights. Companies don't act like humans when they are run well (they are amoral entities that exist to serve limited business purposes to the benefit of investors). When poorly run, they magnify the power of the people at the controls of the company. And "incorporation" is not a natural construct; it's a legal construct. Laws should, IMO, benefit the public first. If we're going to create a legal structure that bestows limited immunity from liability for investors, then why not attach some pro-social strings? For example, we could change section 215 of the DMCA to explicitly state that immunity from liability for user-created content, only applies when the company acts as a common carrier, e.g. they do not have a right to freedom to dissociate with specific customers, and the company by default allows all content with the content neutral algorithm above. The company may ALSO provide their own algorithms for displaying and prioritizing content, but it must be explicit opt-in and able to be opted out of.
If this seems radical, consider that under this suggestion, a company could moderate however they want, but must make it optional; they could also choose to act like newspapers or TV stations and forgo liability protection and moderate however they want and associate with whomever they want.
I'm simply saying that I think it's a fair trade for society to say "if you want all these immunities from liabilities that normal people don't enjoy, then you have to serve all people, even people you don't like".