Do I need to report my 2019 PA state refund of military pay on my 2020 federal taxes because I got the refund even though it wasn't taxable?

If you know it is not taxable, then you do not have to enter it.   Whether it is taxable or not depends on whether or not you itemized your deductions on your 2019 federal return and received a tax benefit for doing so.    If all three of the following are true, your refund counts as taxable income:

• You itemized deductions last year, instead of taking the standard deduction
• You claimed state and local income taxes (not general sales taxes)
• Claiming the deduction helped you increase your federal refund or lower your tax bill

If you are unsure about it, enter the state refund and let TurboTax figure it out.   But if you know it is not taxable, it is not going to affect your tax return anyway, so you are not required to enter it.  

Other related information:

• Where do I enter a 1099-G for a state or local tax refund?
• Did I itemize last year?
• How do I report last year's state or local refund without a 1099-G?