Yes, inmates have First Amendment rights. They even have the right to give the Quran to a prison guard.
The case is Washington v. Gonyea, a summary order issued on September 10. Washington was locked up in the big house when he gave a Quran to Tammi Chaboty, a guard. He alleged in his lawsuit that the prison punished him for this gesture.While the district court threw out the case under Rule 12 because plaintiff did not allege that he held a sincere religious belief sufficient to trigger the First Amendment's freedom-of-religion protections, the Court of Appeals (Chin, Livingston and Ramos) says the complaint alleges that sincerity sufficient to withstand Rule 12 dismissal. The lawsuit says that Washington gave the Quran to Chaboty "in response
to her expressed interest to know about the religion of Islam." He
claimed it was his religious duty to spread the word, "especially to
those who inquire about it."
To win the case, the State has to show that the punishment was reasonably related to legitimate penological interests. That's an easy standard for the State to satisfy. But that argument is not suitable on a Rule 12 motion, before the parties have taken any discovery, the Second Circuit says, particularly since the complaint alleges that Washington was punished out of personal animus and not for any safety or security related objectives.
On this same set of facts, Washington also sues under the Religious Land Use and Institutitonalized Persons Act of 2000, also known as RLUIPA, which gives inmates a statutory right (apart from the Constitution) to practice their religion in jail. Washington loses this branch of the case (producing a separate opinion from the Court of Appeals), because the Court finds for the first time that RLUIPA "does not authorize monetary damages against state officers in their official capacities, and does not create a private right of action against state officers in their individual capacities." This is a sovereign immunity issue, which prevents certain damages awards against state officials. RLUIPA still allows inmates to win damages against local officials.
Washington also sues under the Due Process Clause because he was put into solitary confinement after he lost a prison disciplinary hearing for "communicating messages of a personal nature to an employee." These cases are a dime a dozen, and they usually end in defeat for the inmate. That's the result here. What makes this one interesting is that, after losing the hearing, Washington brought an Article 78 in State court challenging the adverse decision. The Third Department said the disciplinary decision was not based on substantial evidence and was therefore erroneous. But that does not mean that Washington has a Due Process claim, the Court of Appeals says, because lack of "substantial evidence" does not mean "no reliable evidence." Someone testified at the disciplinary hearing that when Washington gave Chaboty the Quran, he did so with an "eerie smile which was unnerving." That was enough evidence to satisfy the Due Process Clause, even it was not enough to put Washington away in solitary under State inmate disciplinary regulations.