Quit a few errors in your reasoning.
1. Churches that meet the requirements of IRC Section 501(c)(3) are automatically 
considered tax exempt and are not required to apply for and obtain recognition of tax-exempt status from the IRS.

2. On of the status of 501 (C) 3 is lobbying!!

3. Unions are also 501 (c) 4, tax exempt and politically active.

4. While limited in their scope ,churches are not forbidden from any political activity. Ad as I said petitioning your government  for redress is NOT political activity