This has happened in the past and liberals and leftists have complained rightfully.
If anything, I'd say the last decade or so has been right-wingers sticking their fingers in their ears and pretending the oncoming train liberals were warning them about didn't exist, right before getting hit by said oncoming train.
You are correct that "big tech is controlled by liberals" (I'd also include libertarians here as well), but in order to be anywhere close to consistent and get what you want you need to also embrace at least some left-wing or libertarian ideas about money and power. Any one of the following viewpoints are reasonable:
Left-wing: Ideological diversity should be allowed up to intersectionality and social media companies should be regulated like common carriers
That Mozilla blog post: Somewhere between the "left-wing" and "left-libertarian" viewpoints.
Left-libertarian: People should switch to federated Mastodon instances run on the basis of mutual aid (e.g. recurring donations or P2P technology) and centralized social media platforms should be recognized as harmful and shut down
Center-libertarian: Something like NearlyFreeSpeech's "Morons Funding the Fight Against Morons" policy, in which we sell server hosting to neo-Nazis and then donate all the profits we made off them to organizations that fight neo-Nazis.
Right-libertarian: People should outcompete monopolistic social media platforms with less paracensored versions and the government should take no action (This appears to be what you're advocating for, although in practice I've seen this tried and fail multiple times)
What isn't reasonable is the right-authoritarian approach, which is to just complain about "being censored" when it happens to only you, and then threaten to repeal CDA 230 if the platforms don't change their mind. (Don't get me started on left-authoritarians, or I'll be here all damned day.) That's not free speech by any definition - either the strict "Congress shall make no law" approach or the more general considerations of paracensorship that I'm trying to build a theory of speech rules around.