This legal definition from the Education certainly makes me think that a church preschool is a school. That would make it perfectly off limits for carry.(6-a) "Private school" means a school that:
(A) offers a course of instruction for students in one or more grades from prekindergarten through grade 12; and
(B) is not operated by a governmental entity.
The preschool offers a course of instruction in one grade. The grade is prekindergarten, which is mentioned in this definition. The church is a private institution and not part of a government entity. Thus, this is a private school. Since a school is part of the law in 46.03, and a private school must be a school, I see this as banned.
I am not a lawyer and could very well be wrong.