One thing that gets me about the people who use "free speech" in this way is the sense of entitlement.
20-30 years ago mass media was only accessible to people with large amounts of money to purchase advertising or run their own media platform such as a TV or radio station or a newspaper. It was closed to everyone else unless you could pull off some stunt to get five minutes of fame and somehow leverage that to deliver a message.
Now you have these vast platforms enabling anyone with a few bucks and cheap computer to potential address millions upon millions of people in near real time. It's completely unprecedented. In many cases these platforms are free as long as you comply with some minimal platform rules and regulations around what you can and cannot say. For most platforms the rules really are pretty minimal. Twitter is one of the least restrictive. You have to be a real obnoxious ass to get kicked off Twitter.
Somehow people have become so accustomed to this free and ubiquitous open access mass media that what was just a few decades ago impossible is now seen as an entitlement. Refuse to let your platform be used to deliver my message? You're censoring me!
Censorship refers to the use of force to prevent someone from speaking. The government has a legal monopoly on force, so generally this requires a law to be passed or perhaps an abuse of the civil court system to leverage the government to shut down someone's speech.
I can't speak for every country but in the USA that is extremely rare. We take the first amendment very seriously around here. You've got to go pretty far to get actually censored. You can buy books on how to make illegal drugs for example, or slander public figures on social media with baseless accusations, or publish software designed to directly facilitate illegal activity, and rarely will anything happen to you.
Being denied access to speak via someone else's privately owned and operated platform is not censorship. Nobody is preventing you from speaking. They're just refusing to assist you in delivering that speech.
Imagine someone walking into a newspaper office 40 years ago and demanding to have their op-ed printed (for free!) and then shouting "censorship!" when the newspaper refused? It's ridiculous.
I thought conservatives were skeptical of entitlements, especially when they involve other peoples' property.