The Free Speech clause in the First Amendment limits the government's right to act against speech. But it's not the only clause there.
A private website is not a town square. The relevant thing is freedom of the press.
So in fact, the First Amendment says a great deal about companies limiting user speech. Companies are legal persons and have the right, in fact the obligation, as I'll discuss.
Freedom of the press belongs to them that own presses
And the press belongs to Facebook, Twitter, Reddit et.al and they can put anything they want on it, with or without you.
Of course, that's not what the users want to hear!
Freedom of the press used to be a big deal when a press cost several years' wage. But last I looked, GoDaddy sells presses for $12.99/year. So there's actually a market solution to the free-speech problem you are discussing, and that's for someone to form their own social media site, and use their genuine free press to delegate to users their own freedom of speech. If the market values that, then this site will win.
However... That has limits
Courts have historically given platforms wide latitude to manage UGC (User Generated Content) consistent with the health of their platform. As someone who managed content for a large social media company, it's our job to put the platform first, so we achieve our business goals (which tend to be asymptotic to providing a great user experience overall, i.e. on average for the public at large, not Joe Nut's throbbing ego.)
Anyone else running a UGC social media platform will inevitably have the same problem: user activities will conflict with the health of the platform and you'll have to deal with it. When your business runs on UGC, it's not an option to manage it; it's mandatory.
Ultimately, the answer is for users to own their own presses.