I don't have time right now. This line of debate is irrelevant. It is still not private property. The "church" would not own it. It is still within a GFSZ (felony violation) and likely still considered within a school building which would fall under other local ordinances or codes regarding weapons.
http://legis.wisconsin.gov/lrb/gw/gw_12.pdf
http://legis.wisconsin.gov/statutes/Stat0120.pdf
I would not want to be the one facing a citation ffor 941.235 and having my only defense be that a School Board is not a "Political Subdivision" of the State and therefore a building owned by them is not a "public" building...
School districts are not political subdivisions, which consist of cities, villages, towns and counties. School districts are, however, "local units of government"-- which includes all political subdivisions plus special purpose districts such as school districts, sewage districts, baseball stadium districts, et al.
In the case of school buildings, the GFSZ doesn't make any distinction between publicly and privately-own schools; a school is a school, and the law applies the same in either case. I don't think renting or using part of a school building for a non-school purpose, such as church, would change a thing. The school still owns it.
I imagine a different case could be made if you found a building that was partially owned by a school and partially owned by a private non-school owner. Perhaps the non-school owned portions would be regarded as any other private property within 1000' feet of school grounds.
I doubt we'd find an instance of such a building in Wisconsin, and if there is, then I can only think it's quite rare.