The House just passed a bill that could politicize churches

Great, more BS from the political world.

Politics plays a heavy hand in religious affairs, from electing leaders to obtaining approvals from the State for Parishes or Diocese; from being elevated to a Saint to electing a Pope.
Religion definitely dabbles in politics and it's leaders are close to royalty that these leaders are regularly seen providing political advice with religious spins.
Church is within the State, so the laws applied by the State applies to the Church. However, the rules of the Church must be derived from the laws of the State, but not necessarily visa versa. The Church is made up of people from the State, but the makeup of the State doesn't need to include Church. State officials are elected by people of that State, but Church leaders are elected by their Parishes and the Diocese. There is separation of State and Church, yet Church and State are joined.

There is no separation of church and state in the Constitution. The Bill of Rights forbids Congress from interfering with the practice of free exercise of religion. It does not prohibit religion from interfering with politics.