The question largely depends on the jurisdiction in which the penal institution is located. In the United States, prison wardens do not have the authority to grant or withhold a prisoners' rights, as rights are—by definition—inalienable. While persons under a judicial sanction may forfeit rights, such forfeiture is defined in constitutional and statute law and not by executive fiat.
However, a warden can grant or withhold privileges or determine the method by which rights can be safely exercised in the prison environment. And, the warden generally has the authority to impose a "neutral" rule—one that is not specific to any particular religion—and apply it throughout the prison even if, to do so might interfere with the ability of specific prisoners to practice a specific religion (see Oregon v. Smith). For example, a warden can require invasive, bodily searches of prisoners for contraband even if the religious beliefs of some prisoners might be transgressed by such a search.
That said, prisoners are permitted to practice a "sincerely held religious belief." To be "sincerely held," a belief system has to be genuinely subscribed to by its adherent who practices and follows its precepts consistently. For instance, in Vaughn v. Garrison, the Supreme Court determined that a prison could deny a prisoner's request for accessories typically associated with the practice of Islam—such as a prayer rug—if they did not first request a pork-free diet.