We are not set up to provide automatic shipping updates, so I would like to remove the section of the order confirmation page that promises we'll send them. I can't for the life of me figure out how to do it - some help content suggests it can be edited but other help content says it can't be disabled.
Merchants cannot access or make changes to the code of the Shopify checkout unless they are on the Plus plan. There's still a workaround. You can change the wordings in the theme language so it won't mention order updates:
From Shopify > Online Store > Actions > Edit Languages.
Type in "updates" for searching and you'll be presented with several textboxes that contain "updates"
Navigate to the section you want and remove this text.
Alternatively, you can use 3rd-party app to customize the Thank You page. Here's an example.