Even if the US, peer pressure is often enough to get political dissenters banned from their social media accounts, jobs, etc.
Many people use the cope out that it's different when it's done by the government or by a private company, but I don't see it as being that different.
With your apparent standard for freedom of speech, isn't pretty much every country excluded? So now everyone is the same as an authoritarian one-party state that outlaws opposition parties and actively censors all internet websites.
Many conservatives or "alt right" types get censored in the west, and some of them have to find hosting in Russia (or on Russian social networks like VK), a country we condemn for censorship. I'm not under the delusion that Russia hosts those people out of respect for freedom of speech, of course, but I find it an interesting observation.
It's hard to blame China for censoring people it deems terrorists, separatists, enemies of the state or whatever, when in the west we're so quick to do it with the enemy-du-jour, sticking a label like 'Nazi' to demonize them (currently, it's the far right/alt right, previously it was communists, who knows which group it will be in ten years).
In addition, the few people and organizations that have been deplatformed from social media and other hosting solutions in the west have had that fate befall them due to companies making a decision that it is not in their financial interest to allow that type of content on their platforms, given its unpopularity among other customers.
This is a completely different situation to China, where companies are directed by the government to explicitly censor certain types of content, and individuals are routinely arrested and imprisoned for creating or sharing content that the government does not agree with.
"Angry mobs", as you put it, are just ordinary people freely expressing their opinions to companies that they choose to do business with. No company is forced to comply with the requests of an "angry mob". No government agency is going to punish a company that doesn't comply. Nobody is getting thrown in prison for something they said online.
Please, it does a disservice to those who are actually experiencing real oppression at the hands of an authoritarian government to make this comparison. Here is just one list of people who have been imprisoned in China largely for expressing themselves online: https://www.chinesepen.org/english/category/writers-in-priso...
Meanwhile, the "many conservatives" who you suggest have been censored in the west are still free to broadcast their content to anyone who wants to listen.
We were talking about people being banned/censored/"de-platformed" from social media companies, in China and in the west. I'm aware that, otherwise, human rights abuse are way worse in China.
As for the idea that abuse only matters when done by a government, it's absurd. We're seeing now private companies talking about censoring the US President, so it's pretty clear who has most power. You can hide behind technicalities like them being private companies or whatever (I note that this argument does not hold when a small mom and pop company refuses to bake a cake, but apparently much larger companies can do whatever they want), but it just means that those companies have the power to censor speech _in practice_ (which is what actually matters in the end), and at the moment they're following angry mobs and not elected officials to define those censorship policies.
A Nazi getting banned from Facebook isnt comparable to a human rights lawyer being stuck under house arrest for years.
America is no better than China when it comes to repressing dissent. American military industrial pharmaceutical organisations are better at usurping insurrection and revolutionary movements, however.