I called OSBI and they seem to interpret the law the same as I do. A church is private property and if the private property owner does not disallow it, then it is OK.
That being said however, the law also says carrying is prohibited when the government leases property for doing business with the public. Voting is definitely doing business with the public. I do not know if counties lease space from churches or if the church just does it as part of their civic duty. I tried calling the election board but their phones are busy today, go figure.