I think considering it an actual belief in "free speech" is giving them too much credit. It's a shield the hateful hide behind, that's all. The people screaming loudest about free speech are more than happy to shut down the rights of others.
Do you have an example of this?
The former has many threads that are marked "conservatives only" which auto delete any comments from anyone not tagged as conservative by mods. t_d will just delete your comments and ban you if you dare to speak out against Trump.
And all this is not even counting the downvotes you get for speaking your mind in rightwing or alt right places.
Note, this is not /r/liberalpolitics, or /r/progressivepolitics, but /r/politics, and yet it is an extremely one-sided exercise in herd behavior.