First double check with the manufacturer, that these products indeed have no bar codes, and also check the packaging of the products, there should be a bar code.
If so, fill out the required data. (Brand+GTIN)
If the products don’t have a barcode, remove brand, mpn and gtin values, and set identifier exists to no. Double check what the results are of your rules by going to Google Merchant Center > Products > all products > click on your product > scroll to the bottom and view the final attributes.
If there is no brand, mpn and gtin, and identifier is false or no. And Google complains, then most likely there are valid barcodes in existence as otherwise Google would not complain.