Under Near v. Minnesota it is very hard to "legally restrict" any publication in the US. The "Banned books" linked to in the question have, in some cases, been removed from particular school curricula or from library collections. A few have been challenged as obscene, but none of them are unavailable to the general public at this time.
A work can be "legally banned" or "legally restricted" under US law for only a few reasons:
A work that is actually classified cannot be lawfully distributed. However, referring to it or quoting from it would be legal unless the quoted content includes actual classified information. A problem with this is that one often does not know just what aspects of a document are in fact classified, short of asking the government.
In many cases the restrictions on distributing classified material apply only to those who have accepted a security clearance or otherwise agreed to be bound by the classification system. However under the Espionage Act and the Atomic Energy act, and perhaps other laws, in some cases people who never accepted a clearance may be enjoined from disclosure, or possibly held criminally liable. This was challenged in United States v. Progressive, Inc. 467 F. Supp. 990 (W.D. Wis. 1979) (The "H-bomb Secret" case). But that case was dropped as moot when the information was published by others, and the DoE announced that they would not prosecute anyone involved. No final binding decision on the issues was made.
A\n attempt to enjoin publication of classified information was famously overturns in New York Times Co. v. United States, 403 U.S. 713 (1971) (the "Pentagon Papers" case). In that case the material sought to be classified was historical, not of current operational importance.
A work found obscene under Miller v. California, 413 U.S. 15 (1973) is illegal to distribute. But it is legal to refer to such a book. It is legal to quote it, unless the quoted section is itself obscene under Miller.
Note that content will not be found obscene under Miller unless it violates a specific law, usually a state law. Unless there is such a law, a prosecution does not pass the Miller test. This means that generalized laws such as "disturbing the peace" cannot be used to punish allegedly obscene content.
Laws may prohibit content not obscene under Miller from being knowingly provided to minors, or shown in movie theaters under ratings which would permit minors to enter.
A work containing child pornography is unlawful to create, distribute, or possess under 18 U.S.C. §2251 and subsequent sections. Quoting a part that includes child pornography as defined under those laws would be equally illegal, but quoting a part that does not include such content would not. Referring to such a book would not be illegal.
Note that in the US only actual images of real children constitute child pornography. Drawings or computer images not based on any real child, and text, may not be banned under these laws. In some other countries, such content may be highly illegal.
Republishing a work found to be defamatory would in many cases be defamation also, and could give rise to a successful lawsuit, but it is not a crime. A quote that did not include any of the defamatory statements would be lawful. A quote that did include defamatory statements may be protected under some circumstances, such as news reporting of the court case. It is lawful to refer to such a work.
Criminal libel was once common, but prosecutions for it are now very rare. According to the ACLU:
Twenty-four states have laws that make it a crime to publicly say mean things about people, with penalties ranging from fines to imprisonment. These laws violate the First Amendment and are disproportionately used against people who criticize public officials or government employees. The ACLU has filed a lawsuit challenging the law in New Hampshire.
According to Wikipedia:
Criminal libel is rarely prosecuted but exists on the books in many states, and is constitutionally permitted in circumstances essentially identical to those where civil libel liability is constitutional.
According to The First Amendment Encyclopedia's article:
Although libel or defamation is now primarily a civil claim, it once was primarily a criminal offense, prosecuted by the government and punishable by imprisonment or a fine.
In the United States, courts have based decisions regarding slanderous or libelous statements on the First Amendment rights of free speech and freedom of the press.
There was also a growing sentiment against criminal libel, which led the drafters of the 1962 American Law Institute’s Model Penal Code specifically to exclude the crime of criminal defamation.
[The US Supreme] Court ruled, in Garrison v. Louisiana (1964), that truth must be an absolute defense to criminal libel. The Court also held that the actual malice requirement in Sullivan applied to criminal libel prosecutions stemming from statements about public officials ...
The Court’s most recent ruling regarding criminal libel was Ashton v. Kentucky (1966), which held that Kentucky’s unwritten, common law crime of libel was too indefinite and uncertain to be prosecuted. This ruling effectively eliminated common law criminal libel.
In short, while criminal libel still exists in the US it is of very limited importance and rare occurrence. referring to a document publishing a criminal libel is not an offense. Quoting such a document could be an offense if the quotation includes the allegedly libelous statement(s).
Distributing unauthorized copies of a work, or copies of an unauthorized derivative work, may be copyright infringement and be grounds or a successful infringement suit. Referring to such a work is lawful. Linking to an infringing work may in some cases be held to be contributory infringement. Quoting from such a work will in most cases be lawful, unless the quotation itself constitutes infringement. Quoting an excessive amount may itself be infringement.
Note that a valid defense of fair use may mean that distributing copyrighted content is lawful, so that a suit will not succeed. Fair use issues are highly fact-driven, and no clear bright line can be drawn between what is and is not permitted. This seems to be by legislative intent. Fair use was originally a judge-made doctrine, incorporated into the Copyright Act of 1976.
Note also that copyright infringement is usually a civil matter, so that if the copyright holder does not file suit, there is no enforcement. Only in willful bulk commercial infringement are criminal charges brought.
It is unlawful to publish, distribute, or use a trade secret to which one has gained improper access. Under the Uniform Trade Secrets Act (UTSA), specifically section 1.4:
"Trade secret" means information, including a formula, pattern, compilation, program, device, method, technique, or process, that:
(i) derives independent economic value, actual or potential, from not being generally known to, and not being readily ascertainable by proper means by, other persons who can obtain economic value from its disclosure or use, and
(ii) is the subject of efforts that are reasonable under the circumstances to maintain its secrecy.
"Improper means" of learning a trade secret (under the USTA, sec 1.1) include:
theft, bribery, misrepresentation, breach or inducement of a breach of a duty to maintain secrecy, or espionage through electronic or other means.
"Proper means" include: discovery by independent invention, reverse engineering, licensing arrangement, and published literature.
The 2016 US Federal Defend Trade Secrets Act (18 U.S.C. § 1836) and the earlier US Economic Espionage Act of 1996 offer protection to trade secrets on a federal level.
Note that like copyright, violation of a trade secret is a civil matter, not a crime. If the owner of a trade secret does not file a suit or take other legal action, there is no enforcement.
It is not unlawful to refer to a trade secret or a document that discloses one. It is not unlawful to disclose a trade secret that has already become public knowledge, although an actual document may well be protected by copyright.
Simply referring to a work is almost never unlawful. Quoting from a work that is actually legally restricted will generally only be unlawful if the quoted content alone violates the same law or is on its own the same tort.