The libertarians generally do (god the mental gymnastics are great when this is not the case though); The mainstreams conservatives tend to mostly support it until their pet issues come up; I support it online because I fundamentally believe my views are correct and will win out on a truly open platform so I don't need to censor others, but I don't believe in inherent rights truth be told.
Now I assume if it has not already this thread will quickly devolve into no true scotsman arguments as everyone argues what a "Conservative" even is.
You assume rightly, but I came here to devolve it into a no true scotsman argument as to what a "right winger" even is. These terms are very silly and don't tell you anything of value except who you're supposed to dislike on voting day- in America. On the internet, it makes even
less sense to use them, since the American "right wing" votes "left" in France and Germany, is too "right wing" for any party in Britain, and there's an array of separate parties for each sub-group of the "right wing" who all hate each-other in Italy and Greece.
Libertarians as a rule agree with free speech. This is commensurate of the position as the voter agrees with it.
Conservatives do not believe in establishing additional constraints on behavior outside of the ones that were implemented in "the good times". A few decades ago, speech was freer than it is today, so they support free speech within that context. This is commensurate of the position as the voter agrees with it.
"Left wingers" are also pro free speech on principle, it's just that there aren't many of them left. They've been choked out by hippie neocons and tankies. If you disagree, hit me up when any given "left wing" senator, justice, or president in the US moves to ratify the Citizen's Initiatives, roll back restrictions on gun ownership, or push an alternative voting system that doesn't viciously disenfranchise voters on the federal level.