Why am I being charged Arizona state income tax? I am an active duty military service member.

You are correct AZ does not tax active duty military pay.  First be sure you have indicated in the "My Info" section that you are "Current" military.  Additionally, if AZ is your home of record be sure it is listed as your resident state. 

If AZ is not your resident state, but you are stationed there it should not be listed as a state of residence at all in the my info section.  If you did not have any other AZ source income (side job or rental for example), then AZ will not be listed on your return anywhere. 

Also, check that when you entered your active duty W2 that you indicated it was active duty pay in the follow on question.

As an AZ resident when you work the AZ state interview, you will arrive at a page titled, "Active Duty Pay is not Taxable".  It will occur right after the dependent questions.  There you will have box to enter your active duty pay to be excluded from AZ taxes.