Sorry, it is not axiomatic. It’s a little sematic game your playing that tries to paint any expression of thought or idea that is not an explicit affirmation of God as a denial of God.
OK!...Then it should be **easy** for you to describe a religiously neutral school.
Again the following are only a **few** of the issues you would need to address:
*What days will school events be scheduled so that all students have an equal opportunity to participate and that no godless or God believing student is favored or disfavored? Friday evening? Saturday? Sunday?
*Is the school co-ed or single sex?
*Will the school allow other children to tempt some children with highly fashionable clothing that is proscribed by their religion. Will the girls wear skirts or slacks? Will the boys have short hair or long, and will their faces be shaved or will they wear beards?
*Does the curriculum have a godless or God-centered worldview?
*Which foods will be allowed or disallowed. Will the teachers and other students be permitted to tempt children to eat delicious foods proscribed by their religion?
*Will music and dancing be completely proscribed or allowed. Will some students be allowed to tempt other students with music and dance that is forbidden by their church leaders. What religious music will be allowed or disallowed? Which religious music will be studied in depth, merely mentioned, or completely ignored?
* Will art be permitted or forbidden? What topics will be allowed or disallowed?
*Which theater productions will be allowed, disallowed, or merely mentioned?