If you bring an Apple ID to the store that exists (instead of making a new one), you are not presented with the None option.
Try the following steps as a work around:
- Try to purchase a free item in the iTunes or Mac App Store on a non-iOS device
- Log in when prompted
- Accept any terms you have to
- If None is not an option on the Review Payment Information screen, click Paypal
- Click the To redeem a code, click here link that appears below
- Log in again when prompted
- Accept any terms you have to again
- The new Review Payment Information screen should allow you to select None
Alternatively, clicking Redeem in the Quick Links box on the main page of the Mac App Store may allow you to bypass steps 1-5. You also can just put in payment method one time, do not make a charge and then remove it.
Lastly, someone that's a family organizer can ask you to join and then you would leave once your account is "verified" into the app store.