The Left Thinks the Right Struck First
One reason the Left is so eager to impose their opinions is that, in some sectors, the Right struck first, sometimes without realizing it. For example, one characterization of moderates is that they might claim:
If conservatives use the power of the state to end drag-queen story time in public libraries, what will stop progressives from using the power of the state to end prayer in public schools?In this case, prayer in public schools was an earlier example of imposing opinions.
Similarly, the current proposals to classify those social media that censor the “alt-right” as publishers (and therefore legally responsible for anything illegal on their sites) is a matter of repealing earlier laws that made it for social media to censor pornography without being classified as publishers. Leftists believe “You said our stuff was obscene? Okay, we say your stuff is obscene!“