In the second season episode of The X-Files "Red Museum," Mulder and Scully visit the home of a devout vegetarian, Odin, who refuses then access to his house because they eat meat.
They don't have a warrant, and Odin states that even with a warrant they would still be denied entrance to his house under the First Amendment.
How would this actually play out?
Religious protection from federal warrants is not a First Amendment issue. If protected at all, the best argument would be in RFRA, the federal statute implemented in 42 U.S.C. §2000bb-1 et seq.
It provides that the "Government shall not substantially burden a person’s exercise of religion..." except if the burden "is in furtherance of a compelling governmental interest and is the least restrictive means of furthering that compelling governmental interest."
It is my guess that every court in the U.S. would agree that a search warrant issued upon probable cause is in furtherance of a compelling governmental interest, and having an agent or two walk through the house (or whatever is necessary in order to exercise that warrant) is the least restrictive means of furthering that interest.
A subject's religion, house rules, etc. are simply not a consideration in the issuance and execution of a search warrant. A warrant authorizes officers to take whatever measures they consider necessary to safely search for and secure whatever is being sought. The only variations in a search warrant are whether:
A subject and his property have virtually no rights in the face of a warrant – certainly no rights to impose rules. See these previous questions.
You are talking about a vegetarian. I don't think you have particularly strong rights against people discriminating against vegetarians, unlike discrimination against gender, race, religion and so on.
Now a search warrant gives the police the right to search your house. I can't see how this would give a police officer the right to eat in your house, or to have a nap on your sofa, or to use your toilet, or to watch TV in your house. On the other hand, if he or she does, you will have a hard time doing anything meaningful about it.
On the other hand: Say a police officer comes with a search warrant that allows him to search the home of a devout muslim for suspected illegal drugs. The police officer demonstratively eats a bacon sandwich in the muslim's home, then finds a significant amount of illegal drugs.
A defense lawyer would have a field day with this. The bacon sandwich eaten in the house of a muslim would be a clear sign of racism (I suspect that police officers very rarely eat bacon sandwiches while they perform a search), and therefore there would be reasonable doubt that the drugs were in the house before the police officer started the search.
