The error "Customers could not be merged because they have different external customer IDs for the same source system. Please unlink one and try again" appears when you're trying to merge two Profiles that may exist in multiple external systems — like different Shopify instances — because the Customer may have used other email addresses in those systems compared to what's in Gladly.
Before merging, try unlinking the Customer Profile to the external systems(s) first. Once unlinked, attempt the merge again.