Not the same kind of suppression, not by a long stretch.
You're still legally entitled to stand on a street corner in the US and shout racial slurs, if that's your thing. You're also legally entitled to assemble and protest there.
None of the undertakings that are equivalent to those actions are permitted in China, and will immediately subject you to violence.
> But there is considerable extralegal hate speech regulation. Your face will be plastered all over social media and you will get "cancelled" and lose your career
That's a pretty convoluted way to say "people in the US don't tolerate assholes".
> and no "free speech" laws will protect you from that
You have a right to speak freely without the government stopping you. You have no right to have people listen to you. In fact the same guarantee that you have for speech also enshrines free assembly.
So everyone who disagrees with your bullshit is free to ignore you and convince others to ignore you. They're also free to boot you off or out of their property.
Yeah, I don't know how America can be considered a so-called "free country" when the people living there will get angry at me for using slurs and being generally discriminative. I'm sure it's just a matter of time until they create some kind of unethical legal punishment too, as they did with expressions of anger (assault, murder, etc.).
Deng was actually in the middle between the hardliners and reformists, from accounts I've read. He wasn't officially head of the party anymore, and there was stalemate for a few days about how to handle the protests before Deng finally weighed in with 'enough is enough'.