I don't think it's a problem as long as the church is not controlling the process in any way.
I vote at a clown school.
I once met a rude woman at a church where I went to vote. The woman was a crabby, dour old b_tch.
This was at some church in Boise, ID while I was living there in the year 2000.
At Christmastime, this church would post a sign out side saying, "KEEP CHRIST in CHRISTMAS".
Anyway, I made a long-winded introduction to this poll worker: "Hello. My name is Jonathan Bailey. I'm here to vote today."
She then looked crabby and said, "What??"
Then I repeated myself, " I said, Hello, my name is Jonathan Bailey and I'm here to vote today."
Then she said "hold on..." while she was looking up my address, name and such.
She did not like me at all.
Years, later while living in Boise still my new were polling place was the Student Union at BSU in town there on campus.
The younger women there were all smiling and cheerful. Of course, I kept my introduction simple by just saying HELLO and showing my precinct card remembering Old Miss Crabapple at the church years earlier. I think I insulted this old hick women by saying too much. These old hicks are slow and simple-minded. I've learned to just say a simple greeting and let the poll workers ask for more information.
The reason I told the bitter old bat at the church that
I was there to vote because I wasn't there to pray. I didn't mean to insult her intelligence. That negative experience at the church has always turned me off to using churches as polls. Many crabby people are churchgoers. I've seen crabby-looking old Catholic priests years ago.
I had a crabby younger man with one earring working at Target "customer service" years ago. He got crabby because I returned the merchandise by immediately saying that I wanted my money back. Some store workers don't like to hear off the bat, "I want my money back."