If Im in the Active Military should I still be getting charged state taxes. Are my state taxes included in what the Military already pulls from my paycheck for taxes?

Yes, your military pay may be taxable in your Home State of Record when you joined the military.  As far as state taxes being deducted from your military pay, you can look on lines 15-17 on your W2 to see if your state income was reported on the form and if state taxes were deducted on your paycheck.