There was a time period when the left was for free speech and the right was wanting to constrain it. Maybe its just a giant pendulum - there is no right/left difference when it comes to free speech - everyone wants to censor / filter the speech of the opposite side.
If things come in cycles, then I expect the right to take over more and more (see the european shift) and then for them to slowly become in favor of censorship. Maybe then - if we are lucky - the left will remember that censorship is always the enemy even if it helps them currently.