Your imagining is irrelevant to this conversation. No-one has a "right" to say whatever they want - particularly things that are offensive or discriminatory - without consequences. Private companies don't have to justify why they fire someone or why they hold or enforce the boundaries that they have - unless it is for an illegal reason. Otherwise they have complete discretion to run their businesses as they see fit.
Peterson is all about the dominance hierarchy, but suddenly, when someone with more power has the audacity to impinge on his "freedoms" you are all in a twist about it. You both ought to recognize that if you want a "might makes right" world, you have to accept when you are on the receiving end of that to your disadvantage.