To my mind the problem is that they are conflating different social problem under one rubric of "free speech", where they don't all fit. Which, indeed indicates they don't have a very clear headed view of what they are talking about. For instance, one issue here is that if anything, the negative reaction to a lot of what they call 'speech' is really just the natural and proper reaction to the lack of both civility, basic competence, and dare we say - sanity, on the part of too many 'speakers' demanding to monopolize the soapbox. It's more a matter of 'please stop wasting my time with your stupidity.' We need *more* social approbation of pubic stupidity lest our general descent into ignorance go completely unchecked.
On the other hand, there is also the soft bigotry of lowered intellectual expectations doing its work in the argument that there are sooo many things we mustn't talk about for fear of melting the snowflakes - whether it be screening Olivier film where he plays Othello in black face or Bobby hearing about Jimmy's two mommies. At any rate, the point is that many of the things they are throwing at the wall in this piece are pretty unrelated.