Q. Can parents deduct school supplies?
A. Simple answer: No. You're getting mixed answers because the real answer is: "it depends".
There is no federal deduction for your child's school supplies. Some states have a limited deduction (usually just tuition). If yours is one, it will come up in the state interview.
A public school would qualify as a charity. As such, anything you donate to them would qualify as a charitable deduction, on Schedule A, of your federal return. It is only an itemized deduction. Only teachers are allowed the (non itemized) allowance ( deduction) for supplies.