Most of these things that aren't a matter of private freedom of association for platform owners tend to eventually get struck down because the Supreme Court can somewhat reliably be counted on to eventually respect the Constitution, but the general public and elected politicians have never supported free speech or free anything. I would say almost the exact opposite of what you said. People only claim to love free speech when something they want to say is unpopular or suppressed. Almost nobody just supports it generally. The ACLU used to be pretty reliable about this, i.e. defending the KKK and Nazis, but I'm not even really sure where they stand any more.
The average citizen doesn't give a crap about any abstract ideals at all. They just want to live their lives and possibly raise a family in an atmosphere not dissonant with their own cultural traditions and beliefs. Allowing people with other traditions and beliefs to spread those via public advocacy, art, or any other means that may lead to them being mainstream or even dominant is antithetical to that.