People are alarmed by these moves because they represent a wider trend in which the left increasingly does not recognise the right as politically legitimate, i.e. they do not believe non-leftists should be allowed to exist. Tech firm activist censorship is merely one visible (or not so visible) aspect of this. But it's not the only aspect.

The very same sorts of people with the very same views are also in government institutions in abundance, as we've seen in recent years with the descent of the various left-wing elites into conspiracy theories about Russia - theories that were then used to try and effectively block implementations of public votes, on the belief that surely the public could not possibly reject their enlightened governance unless they were being manipulated.

This isn't purely a US thing. The UK has the same problems. Recently one of the government's advisors on COVID was complaining (on Twitter!) that the BBC had agreed to unfairly rig a debate she was involved with, but hadn't properly enforced that rigging:

https://twitter.com/SusanMichie/status/1311234012283899904

A lot of the British political class lost their minds over Brexit. You saw incredible things, like politicians running as candidates of the party saying they'd implement the decision, and then switching post-election to the party with saying they'd void the vote and never leave. They had flat out lied to voters about their intentions. That happened quite a few times. There were many other tricks deployed too. They fundamentally didn't believe in the legitimacy of their political opposition and were willing to manipulate the electoral processes to try and "win" despite having lost at the ballot box.