The App Store is country specific.
If you are signing in to the store for your country it would not be requesting a postal code since it would know there are none for your country.
If you are signing in to the store for a different country, there is nothing you can do, as that different country does use postal codes, and would require it for a valid Billing Address for a payment method from that specific country.
You cannot use a billing method for a different country to the country for the store you are trying to sign into.