In the US, and in this particular decade it is true that the left is keenest on actual politicking to create censorship. But in terms of the human weakness of not wanting to hear arguments against your own POV, then the right is at least as bad.

I think the difference behind the political fireworks is this: conservatives already revel in sub-communities like churches where they can protect themselves from unwanted speech. Progressives are starting to dominate open places like universities to the extent that they want the same privilege there.