Does Arizona require you to pay a school tax even if you are childless?
I have never heard of a specific "school tax"
per se.
As I understand it the educational system is paid for by property taxes. I think the various school districts get some kind of state subsidy which varies by district and which could come from either sales tax or state income tax. However the vast majority of public school funding comes from property tax.
Obviously you don't pay property taxes if you don't own property, and the amount you pay is not at all affected by your child status.
Child status indirectly affects how much sales tax you pay, since typically if you have more children you'll buy more things and pay more sales tax.
Child status REDUCES the amount if state income tax you pay. More kids equals less tax.