No. I don't seriously think China is following the US. They'd do it anyway. But with the US no longer standing as a working example of a country that values free speech there is less need for China to pretend on the world stage to save face and hide their nature. This lack of pretending has become very obvious in China in the last ~5 years. Maybe that's a good thing but the regression in the USA isn't.
Sorry if my original post was a bit glib. The point wasn't to say it's okay for China if the USA does it. My point was that it's an almost universal bad trend in nation states today.