In the United States, most churches file papers of incorporation and formally apply for 501(C)3 status. A few choose not to, a notable example being the Indianapolis Baptist Temple Church in Iowa whose building was seized by IRS in 2001 for a related issue. They had no Employer Identification Number, as they refused any form of government registration. Please ignore the details of the tax case as it's not related to the question.
There are many groups historically which tried to avoid being entangled with the government in any way. What groups today advocate refusal to file these basic documents?