With the postcodes that have been entered on your Local delivery settings within the Shopify admin, do they follow the format listed on ourHelp Centre document here?
Are you also using a third-party app to configure your shipping settings, or have installed or uninstalled a third-party app recently that you think may be impacting how your checkout is performing?
Have you or a staff member of your store also made any changes to your store's theme coding recently?
If you aren't sure, to test all of this out you can install a fresh copy of Debut, re-test your checkout and see if the issues persist. If they don't and you're able to select either store pickup or local delivery ok, there may be some codes on your current theme that is preventing your checkout from loading or performing as intended.
Alternatively, our team can also take a look at your account to further help you in this matter. While we're not able to provide account-specific support via the Shopify Community Forums at this time, we’d be happy to continue assisting you. You canvisit our Help Centre here, and log in to your account to create a support request.
Kimi | Social Care @ Shopify - Was my reply helpful? Click Like to let me know! - Was your question answered? Mark it as an Accepted Solution - To learn more visit the Shopify Help Center or the Shopify Blog