I believe it is actually folks on the right who posture as morally superior on the free speech issue.
They act as if any organization not willing to extend a platform to odious viewpoints, such as white nationalist folks carrying swastikas, turns that organization into the true “speech tyrants”
In reality, private organizations and channels do not owe a platform to any particular person or any viewpoint. That includes TV channels, radio channels, and internet sites like ImgFlip, Twitter, and Facebook — although there is an argument that the largest sites and social media platforms are better thought of as public fora.
But most of the time, saying that Person A should be compelled to platform Person B’s viewpoint is actually tantamount to trampling on Person A’s First Amendment rights.
Despite all the contentiousness over “free speech,” very very few people out there are actually being silenced. Just told to take their opinions elsewhere. Which has been going on for a very long time, long before SJWs existed.
The issue that gets lost in the shuffle, in my opinion, is the importance of *quality* speech and respect. And speaking out against bigotry is a part of that.