I'm so far right that I'm disappointed with Trump. He's a centrist, not right wing.
As for censorship, it's absolutely done more often by the left wing. Protests, social media bans, forum bans, political correctness, narrative control, MSM propaganda. Book bans. The BIble is banned from schools. Harry Potter is protested against. I could go on.
But I've found lots of left-wingers use projection to attack the other side. Everything they do, they accuse conservatives of doing, and I think they even brainwash themselves into believing it.