Like a lot of different states in a lot of different ways, Ohio has it's share of poorly written and/or outright stupid laws.
In Ohio, any business can place a legal "gun buster" sign and nobody other than police officers can legally carry concealed in them. You are permitted, no matter what their sign says, to legally keep your firearm in your car.
Churches occupy their own odd little spot in Ohio, however. They do not have to post a sign to ban concealed carry in the church. It is legally assumed that carrying in church is illegal unless you have specific consent from the church, or the governing body of the church.
In Ohio, those folks who happen to be shooting pals with their pastor, or know someone on church council typically get the "okay" that makes them legal.
For normal average carry-permit guy (me) I may not legally carry unless I first approach the leadership of the church and get consent. So I have three options:
1) "Out" myself to the leader(s) of the church and ask permission, wondering if they'll say, "Cool, we do!" or "you want to WHAT?! WHY?"
2) Break the law and carry without consent, risking a felony and jail time, fines, lawyer fees, and my right to carry concealed and (with a felony), likely my right to own firearms at all.
3) Sit in church and hope it doesn't get attacked while I'm there.