The location of voting booths in churches is a result of an agreement reached between churches and the governing body. I do know some churches/private schools charge a fee. Public facilities, such as public schools cannot charge a fee. As I best recalled from my newspaper reporting days, there is a multi-year contract involved so the polls are not move from place to place each year. While the voting machines are located on private property, all the appropriate state and local laws regarding campaigning, access, etc. have to be followed.
Did you know that in western society the first buildings , outside of a home in villages , as they became more advanced , was a church ! The meeting place other than a home . or a stadium ! Seems pretty normal as to our history . Those who are more Non- spiritual probably find it weird though .