In the US, the right is closely aligned with white evangelical Christians. A large portion of their platform is dedicated to ensuring all Americans must hold the same moral code as that small group. They also actively suppress minority opinion through gerrymandering, voter roll purges, and voter idenfitication requirements. Conservative media isn't operated by the state but it's so tightly interwoven with conservative leadership that it might as well be. Fox News, Breitbart, and the Sinclair Broadcast Group all push decidedly right-wing messaging under the guise of journalism. Trump's EPA is censuring scientists. Trump's FCC is ignoring citizen outreach. Recordings of the White House press briefings are no longer allowed and Trump has called the media "the enemy of the people".
Republicans control the US government through what most on the left consider illegitimate means. The way they hold power is decidedly anti-democratic. They've gotten to a point where they control the day to day narrative and don't even have to listen to opposing viewpoints as they govern.
Texas Lt. Gov Dan Patrick just said this:
> "People are happy with their governments at their state level, they're not with the city," said Patrick, a Republican, in an interview with Fox Business Network. He was responding to a question about gubernatorial races.
> "Our cities are still controlled by Democrats," he added. "And where do we have all our problems in America? Not at the state level run by Republicans, but in our cities that are mostly controlled by Democrat mayors and Democrat city council men and women. That's where you see liberal policies. That's where you see high taxes. That's where you see street crime."
Ignoring that crime scales with population everywhere, people live in cities, cities are centers of production for most states, cities are generally healthier than suburban/exurban/rural areas, and cities are absolutely not happy with republican state governments, this comes on the heels of a series of anti-city legislation at the state level. The Texas legislature has been actively undoing liberal policies in Austin for no reason other than ideological disagreements. We apparently can be overruled at any time by rural legislators from hundreds of miles away.
Suppression is censorship in aggregate. It's not exactly "your opinion is harmful so stop talking" but it sure feels like it, and has the same results. The aggregate form happens to be easier to hide because it is more abstract.
Classic quote by Republican strategist Lee Atwater:
> You start out in 1954 by saying, “Nigger, nigger, nigger.” By 1968 you can’t say “nigger”—that hurts you, backfires. So you say stuff like, uh, forced busing, states’ rights, and all that stuff, and you’re getting so abstract. Now, you’re talking about cutting taxes, and all these things you’re talking about are totally economic things and a byproduct of them is, blacks get hurt worse than whites.… “We want to cut this,” is much more abstract than even the busing thing, uh, and a hell of a lot more abstract than “Nigger, nigger.”
P.S. The dichotomy of state vs private censorship among parties is a false one. I've seen multiple references to a contemporary "red scare" in this forum today. It concerns me that if I were to bring up Russian collusion and election interference I might be shut down as a fear-monger when the concerns are completely valid. I also understand the Republican viewpoint of states suppressing opinion when it comes to things like affirmative action, political correctness, etc. There's too much noise right now for anyone to take anyone else seriously. Hard to imagine that ending anytime soon.