What law other than the Johnson Amendment "requires" churches to remain out of politics? Note that this law is rarely enforced anyway, so there is plenty of political activity in churches. I'm wondering where you get the idea that churches stay out of politics entirely - Hillary Clinton spoke at church services, including the Sunday before the election http://philadelphia.cbslocal.com/2016/11/06/hillary-clinton-speaks-at-philly-church/

If you look at history, tax exemptions for churches started pretty early - Virginia exempted churches from paying property taxes in 1777, followed by New York in 1799 and the city of Washington in 1802. The Seventh Congress also passed a property tax exemption in 1802. Churches were made officialiy exempt from income tax in 1894 when a federal income tax was first proposed http://www.taxhistory.org/thp/readings.nsf/ArtWeb/CFFB1CE42BEFA8B285257BE400723DF8?OpenDocument