Allowing a private and/or religious building to host voting machines for elections unfairly biases the votes. The powerful subliminal message being conveyed to voters is: "This government is given its authority in this church, and you should vote accordingly."
This is a message that violates the Establishment Clause of the First Amendment.
There is no shortage of civic buildings to use for ballot-casting, and there would be less psychological bias in elections if only these civic buildings were used.