Public K-12 school diversity or lack thereof tends to be determined by its attendance area.
Private K-12 school diversity or lack thereof depends on selection and self-selection factors. Ability to pay tuition often skews SES upward. Religious schools may have less religious diversity.
Public charter K-12 school diversity or lack thereof also depends on selection and self-selection factors, though ability to pay tuition is not a factor (however, high SES parents may be better informed about getting their kids into them, and may have more commuting options for their kids).