Neither side are angels. Neither side really believe in your free speech if you disagree with them.
Now, if you want to argue that the right is currently the greater threat, then sure, I can probably agree with that. The two sides try to push the other around when in power, and play the victim when out of it, and the right is currently in power. And they're currently more aggressive than I ever saw the left be. Still, the left isn't really the side of free speech either.
Only one side claimed to be "free speech absolutists".
But a hypocrite that pays lip service to free speech might be better than someone who openly doesn't care for it. At least the principle remains respected.
I mean, look, there are conservatives who actually do care about free speech for everyone, not just their allies. But the "conservatives" currently in power, who claimed to be "free speech absolutists", seem more interested in control of speech as a source of power, rather than in actual free speech for all.
Don't fall into the trap of grouping into left/right. Individual behaviors must be judged separately: going into crowded spaces unmasked during the high of covid? Bad. Burning down a business? Bad. Getting someone fired for speech? Bad. Etc.
See how easy and clear that is? Nothing about left or right.