The government constraining churches via tax code to engage in only certain types of politicking has the same effect as banning other types of politicking. The Establishment clause is the constitutional law that allows the government to limit the types of politicking that Churches engage in, with the terribly lax 'punishment' of tax exemption revocation to fit the 'crime' of engaging in prohibited political activities by a non-profit (including churches). By applying the standard to all non-profits, the gov't doesn't violate the Free Exercise clause.
You say that the government doesn't limit churches in this way. I'm saying it's 6 of one, 1/2 dozen of the other.