Sounds like an overjumped conclusion:
The types who claim "their words are taking away my freedom, so they must be muzzled" are likely to be, by co-incidence, those who identify as left. This suggests the argument that they aren't quite representing the left's tone precisely, for that act.
You're unlikely to meet many who advocate absolute free speech. For one, most acknowledge front violations, eg yelling fire in theaters is prohibited because endangering people is prohibited, preempting speech concerns. For another, most acknowledge that outright threats of violent acts or flagrant libel should be addressed in some capacity.
Those points still leave us a lot of gray spectrum between carte blanche and unquestioningly putting gags on every person./strike> "troll" disfavored by whoever's pulling the scene's levers. Who are often hounded, you might even say harassed, by our noble armchair crusaders.