Maybe across all time, yes. But parties change. Right now there's a clear enemy of free expression, and it's not the right.
The correct play, of course, is to pressure the party that's currently on the anti-free-expression side to back down - even (especially) if that's your "own" party (not like the two major US political parties are very representative of their ostensible constituents) - and that's what the GP is doing.
(you can do this without condemning the ideals of the party as uniformly bad - which is something that a lot of people don't get - attacking a party is not the same as attacking its ideals!)
Are you sure about that[1][2][3]? People on the left side of the aisle seem to be invested chiefly in social shame; the right side is actively using the power of the state to control public expression and educational content. Equivocation between the two feels like false balance.
[1]: https://apnews.com/article/florida-race-and-ethnicity-govern...
[2]: https://www.aclu.org/legal-document/bert-v-o-connor-complain...
[3]: https://www.pewtrusts.org/en/research-and-analysis/blogs/sta...
Conversely, even without me digging up any references of the progressive politicians also using the power of government to suppress free speech, it seems like you're making a false distinction.
Progressives are using their power to try to get people fired and unemployable (which is somewhat disingenuous to call "social shame"). When you can make someone unemployable in most of an industry, there's little difference between that and using the government directly. Furthermore, progressives use large tech companies (with power comparable to the state in some respects) to censor speech on their de-facto-town-square social media platforms.
(FWIW: conflating "progressive" and "left" belies a fundamental misunderstanding of left-of-center politics. It's a misunderstanding that you're going to want to correct if you want people to entertain your positions.)
The sheer hypocrisy of it all is incredible.