You're going to have to get into specifics, I doubt "a growing bipartisan antiliberal movement" is responsible for the categorical removal of free platforms from the internet. This seems like a framing designed to avoid necessary context or mischaracterize motives.
If you mean, for instance, Kiwifarms - their ISP and Cloudflare refused to do business with them for reasons other than being "antiliberal." You can't blame opposition to heinous behavior, or not wanting to do business with or be associated with KF, on simply being opposed to free speech. But they still exist, AFAIK. Gab was similarly "cancelled" by their host and service providers, because the platform itself and its behavior had become too toxic to be associated with, and violated terms of service for those partners.
Again, free speech doesn't guarantee a platform - it's a marketplace of ideas and you have to convince people your ideas are worth their time, doubly so where business associations are involved. Gab was fine until they started planning an insurrection and cheering on mass shooters. Trump was fine until he lost his mind and threatened the peaceful transfer of power. Omegele was fine until someone sued over the one thing Omegele is known for. There are always limits, everywhere. There are plenty of reasons to not want to be associated with such platforms and their content besides opposition to freedom of speech, but conflating everything into the actions of an "antiliberal movement" seems like bad faith.
So I don't know. You see attacks on free speech, I see the inevitable consequences of bad actors pushing things too far.