If I change my store theme, will it affect what I’ve set up in the app?

No, if you change your store theme this will not affect anything you have set up in the Postcode Shipping app.

All of the rates and settings you create in Postcode Shipping operate independently from Shopify, and the app simply displays your shipping rates in the standard checkout flow. This means the rates aren't affected by the theme or vice versa. 

So, feel free to update your store theme whenever you want; everything in the app will remain the same.