Churches really don't need to ask for tax exemptions. The Constitution provides for "free exercise". That means "no taxes". Your question is meaningless.
Individual exercise, yes, but that doesn't necessarily mean churches. Besides, Congress would have to pass a law exempting churches from taxes (since the default state is that everybody gets taxed), which would be a law respecting an establishment of religion (religious establishment).
Still, you're getting off-topic. When a party to a court case puts religion on the table, then of course a court has full authority to look into it.
LBJ successfully muddied those waters, making quasi requirements that Churches register for tax-exempt status. LBJ successfully turned what was once considered a right guarenteed by the Constitution, into a right granted by the IRS. Really sick how the Constitution can get so easily twisted.
Besides, how can the government know they're a church if they're not allowed to ask about the church's religion?