Do churches in the US have any special legal protections beyond that which a 501(c)(3) would have? Religious organizations tend to have some immunities in the US, so I'm wondering what, if anything, carries. Tax stuff, maybe? I think there's a ?myth? about that states that searching a church is illegal?
The US does give deference to organizations that claim to be "religious", for example the Religious Freedom Restoration Act, which "Prohibits any agency, department, or official of the United States or any State (the government) from substantially burdening a person's exercise of religion even if the burden results from a rule of general applicability, except that the government may burden a person's exercise of religion only if it demonstrates that application of the burden to the person: (1) furthers a compelling governmental interest; and (2) is the least restrictive means of furthering that compelling governmental interest." Or the Burwell v Hobby Lobby case based on that law "allowing privately held for-profit corporations to be exempt from a regulation its owners religiously object to, if there is a less restrictive means of furthering the law's interest", or Scientology being allowed to not follow minimum wage, or how Title VII of the Civil Rights Act states "This subchapter shall not apply to an employer with respect to the employment of aliens outside any State, or to a religious corporation".
The greater the nexus between the conduct and the religious nature of the organization, the more deference is given. For instance, roles classified as "ministry", such as a priest, will be given more leeway than a more secular role such as a construction worker who happens to be building a church. BTW, as far 501(c)(3) is concerned, there is deference in that classification, as religious organizations do not have the same burden of establishing charitable purpose that secular organizations do.
Also, having your nonprofit be a church would mean that Immortals wouldn't be able to fight on the grounds.
There is no legal advantage to being a church in terms of searches and seizures, though there may be extra-legal preferential policies by law enforcement agencies, as discussed here. There does exist what is known as the "ministerial exception" which provides an exception to anti-discrimination laws in the hiring of ministers (a Catholic church can require ministers that it hires to be Catholic priests, and they also cannot be forced to hire women priests). This also applies to applies to the wage-and-hour requirements of the Fair Labor Standards Act, and has been applied to the ADA. There is some uncertainty as to who is a "minister". The underlying principle is that the government can forbid various actions, but may have to allow those actions in the event that the prohibition runs afoul of the Free Exercise clause (requiring all religions to hire female priests restricts the exercise of certain religions, just as the prohibition of animal sacrifice restricts certain religions).