The point is the terrible ease of applying a double standard in how you approach an issue.
Some private actor X performs an action Y which other people Z find reprehensible. The action Y is within X's legal rights to perform.
You can focus on how reprehensible Y is and how Z are right to condemn it. Or you could focus on how X should be totally free to do Y if X so desires, even if we don't like Y.
What usually happens is that if you feel Z are right or you wish to support Z or you wish to not be seen as supporting "enemies" of Z, you will focus on condemning Y. It won't even occur to you to emphasize that doing Y is legal; if pressed you'll freely admit it is, but to you focusing on how Y is legal will look like hypocritical attempts to evade the real issue, which is the terribleness of Y.
On the other hand, if you dislike Z or like the "enemies" of Z, you will focus on how Y is legal and how Z's dangerous rhetoric about Y poses a real danger of conflating Y with actually illegal acts. You might or might not agree that Y is terrible, but to you it will seem a decidedly minor concern compared to the dangerous rhetoric issuing from Z.
I wish to see just once someone who makes that argument try to turn it around and apply to something else they don't like to see censored. I'm yet to see it.
The Hollywood Blacklist was completely voluntary on the part of the movie studios which enforced it, a decision of certain private companies not to -- how did you phrase it? -- "tarnish their brand" by collaborating with people suspected of Communist tendencies. It is held to be morally repugnant today, and somehow I doubt you would defend it with the same argument you use in the Dr. Seuss case.
No, it's you who failed to engage with the other commenter's arguments, or failed to understand them. They made the correct point that the famous "banned books week" also typically celebrated, and continues to celebrate, books that were not literally banned according to your definition. Thus this rhetorical extension of "banning books" to cases where books are not literally made illegal to read has a long history, and both detractors and defenders; reading the wikipedia page on Banned Books week is a good way to educate yourself on that history.
In the case of Dr. Seuss books, the near-simultaneous decision of the copyright owner to stop publishing them and of the largest online reselling market, eBay, to forbid selling and buying them, makes them, if not literally banned, vastly more inaccessible than many many other books that have been covered under the Banned Books Weeks event, written about in the media, celebrated by liberal readers (in those prior ages where liberal readers thought that right to read was more important than right to forbid) and so on. Your narrow-minded insistence on literalism is just a way of displaying your ignorance and unwillingness to engage with these difficult questions.