It's always astounding how free speech warriors have a complete lack of understanding what free speech actually is. A private venue deciding not to give someone a platform is in no way a violation of the right to free speech.
I think both 'sides' are too simplistic on the subject.
I agree that the owners of venues have a right to refuse to allow people to air views in their venue that the owners consider inappropriate. We can all think of obvious examples, from neo-Nazi groups wanting to hold a conference on Holocaust denial, to Satanists wanting to book St Pauls Cathedral for a mock sacrifice ritual on the altar. Wholly inappropriate.
Yet at the same time, there have been speakers/performers/comedy acts/etc who have had bookings cancelled by venues after complaints/protests by niche groups for some comments that are innocuous to everyone else - I'm thinking scientitsts who have stated scientific fact about what a woman is. An army of 'social justice warriors' set about creating a furore that spooks venue owners and sponsors, and they pull the plug. When it's universities, which are supposed to thrive on alternative viewpoints, I find it worrying.
It also closes down debates on topics that do interest and impact people in everyday life. It creates a sense of "your views don't matter and should be ignored, because *this* is the othodoxy"
Just as I don't want a society where people are vilified and disciminated against for their race, their sexuality, their gender choices, etc; I don't want a society that closes down debate about issues where people have different opinions and viewpoints - even if I don't necessarily agree with those different opinions and viewpoints.
However, in saying all that, 'cancel culture' is very different from 'call-out culture'. Yet many people on the right-wing delibereately confuse the two, claiming they've been 'cancelled' for 'expressing their right to free speech', when they've actually been 'called out' for expressing an opinion that others disagree with, and who have expressed their own right to free speech by giving their opposing views.