I'd be curious what examples of this you guys have because the biggest examples of attempts to take away the voice of the people all come from the right and they are huge in my experience. We have have had an ongoing massive attempt to take people's right to vote. to throw out their votes, to stop them from voting. That's a rather massive impediment to free speech and it has been conducted through essentially hundreds of lawsuits, fake ballot audits like Maricopa country, and a 24/7/365 barrage from Right wing media and of course the internet. 

Republicans, if you speak out against them or their hero Trump will do all they can to take your job, your voice, and your reputation. Ask Lynn Cheney, Jeff Flake, every single person labelled a RINO. Nobody believes in and loves cancel culture more than the Right.

Watch Right wing media explode daily with some new invented outrage for which they will provide hours of coverage attempting to cancel someone over some asinine/invented nonsense. Then they will pivot to whining about their free speech rights being taken from them because Trump was dumped off of social media and can't spew outrageous lies that incite riots at the capitol, violence, and lunatic conspiracy clans. 

Watch Republicans when they were under Trump actually scrub all words and phrases and ban their use that related to the science of climate change or fighting a deadly virus. Watch Trump, with Republicans cheering, fire people working in defense of our country for using words, phrases, and telling the truth about his misdeeds...to silence their speech. Watch Republicans attempt to out whistleblowers to silence them.

These are all government related free speech issues. 

Where are these on the left?

If a company or a university makes a policy to distance itself from something, that is not a free speech issue. That's a business decision likely run through a legal department or group of attorneys. 

If you guys can give me some examples of the loony left in government shutting down free speech I will certainly be interested and will listen.