I don’t have a solution, but I wanted to leave a comment to hopefully get some awareness.
We are having the same issue. Facebook is not seeing our shipping profiles on Shopify. We finally had a working shop by directing each product to our Shopify product page. Now with Facebook requiring customers checkout through the app and Facebook not seeing our shipping profiles, it is giving every order free shipping. This is probably the end of our Facebook and Instagram shops unless there is a solution found.
Are you by chance using shipping scripts in the script editor? And if so, is one of the scripts related to a free shipping rate that you set up in your shipping profile? That has been the cause of our free shipping issues on Facebook Shop.