It's both.
The left takes great effort to suppress, shout down, and otherwise disrupt the expression of speech and opinions of others that they don't agree with. This has been demonstrated on numerous occasions. How many conservative speakers on universities have their speaking engagements disrupted this way? Does this happen with any such frequency to liberal or progressive speakers on campus? Never heard of such a case, so I hardly think so.
That's fine to an extent, and may very well be an example of free speech countered by more free speech, but you'd expect some respect for others to have their chance to have their say, wouldn't you? So the liberal / progressive intolerance and disrespect of others who hold opinions and ideas that are counter to theirs it pretty clear.
What the left also does is enlist and exhort the government to suppress (censor) the speech of those which they don't agree with. Just look at the excessively PC movement for examples of this. They call for punitive punishment for people that disagree with them, and they cal lon the government to enforce that.
This is BS. And no, it's not legitimate to say that this is the consequences of free speech. It's suppression via authoritarian tyranny. What happened to 'I disagree with what you are saying, but support your right to say it'? Seems that this has fallen to the way side from the liberal ethos, where it was very prominent in the past.
Yes, the liberals and progressives of today are a mere shadow of the what they were previously. Where as previously I would have disagreed with them, I'd at least I could respect them and their position. These days? With their poor behavior and lack of principals? Not so much.