It is my contention that "school, public or private" are referring to schools accredited by TEA or those private schools that TEA recognizes as accredited by their respective organizations (which basically means they are "accredited" by TEA without TEA having to do the visit).
I figure that almost no church pre-schools are accredited if they don't have an elementary school attached with them. I don't imagine any day-care "pre-school" being accredited.
When people are asked, I feel most would answer that a "school" is what we normally think of a school being. Red brick, flag out front, spewing milk through your nose at lunch, books and desks and crayons.
If we really wanted to get picky about it, homeschooling is recognized by the State. Does that mean you can't carry at home? Or what about going to a gun school? Or what if your kids are playing school? Or you happen to be by a lake that has a school of fish in it?
Now I will admit that it gets sticky when a church is housing an accredited school, whether it be the church's or they are under a different charter.
I think that reasonable people, regardless of the presence of a school (by any definition) in a church, will realize that Sunday church activities are not "school" and the building is not a school building.
But what do I know......
I hope this becomes a non-question when the legislation meets this year.