I've e-filed my taxes and am waiting for my state tax to be accepted. I owe a payment, do I pay by the on the due date even if my e-file has not been accepted?

Yes.  Taxes owed have to be paid on April 18, 2023 to avoid a failure to pay penalty. 

If you selected to pay the state taxes owed by direct debit from your bank account and the e-filed tax return is still pending then you have paid the taxes on time.