It seems to me that the basic principles of free speech are not what are in question in these "culture" clashes. Everyone on both "sides" of the debate seems to agree, in principle, that freedom of expression is a necessary component of a free society, even if some opinions are abhorrent to others.
The rubber meets the road when we start to discuss (a) who decides what's acceptable or not, and (b) what's to be done about the PEOPLE holding abhorrent views (not the ideas themselves.)
(a) is really a nonargument. Society decides, ultimately. When common society started reacting negatively to people using the "N" word or telling racist jokes.....those inclined to use the "N" word and tell racist jokes stopped doing so. (Attitudes didn't change, of course --- they simply were driven underground, but that's an entirely different aspect of this debate.)
(We even have SCOTUS rulings along these lines. When it comes to obscenity, the Court ruled that it must lack "serious literary, artistic, political, or scientific value" --- the first two on the list, of course, are determined by social consensus.)
And, of course, (a) has a nuance --- which leads us to (b). Although there is little to fear from a broad societal consensus on what is acceptable and what is not.......not all decisions as to "cancel" are made off a broad societal consensus. If an organization has an employee base which is far to the left or far to the right on a particular issue.....does/should that organization have the moral right to "cancel" the offender? (Brendon Eich comes to mind, here. Of course the Mozilla board had a LEGAL right to terminate him ---- whether that was moral (where morality is determined by the principles behind the Bill of RIghts) is another matter.)
And that situation leads us to the friction with social media. If the social media company is one where the employee base has a far-left world view, they may end up censoring ideas which are uncontroversial in Texas.
And there is also the matter of "activists" (being generous with the terminology, here) forming mobs to prevent speakers from speaking in authorized spaces, even if the speaker has nothing overly controversial in their planned speech; where the reaction is based on the reputation of the speaker amongst that particular group of activists, be that reputation legitimate or not.
Apologies for the ramble, but your article (and Beauchamp's, which I also read) stirred up a lot of thoughts.....and I suspect truth lies somewhere between your article and his (or, perhaps, you didn't mean to issue a blanket condemnation of Beauchamp, but more nuanced one.)