I'm not being snarky, but which instances of the right doing this are you thinking of?

I can recall that in the 80s and 90s, Christian right groups tried to go after pornography (sometimes in alliance with leftist feminists!), but I don't recall the right going after leftist political speech. I guess you could reach way back and talk about the FBI threatening to expose MLK's infidelity and urging him to commit suicide, but I'm not willing to concede J. Edgar Hoover as representing the right (YMMV).

What are you thinking of? I'm not saying it didn't happen.