Not 100% sure if this is a bug or a risky feature.

When you create a PIM product category, you're asked to fill in an identifier field. Then, when you add a translation of that category, you're free to update the value of the identifier.

This is unlike the behavior proposed out-of-the-box for the same taxonomies core mechanism for tags. When you translate a tag, identifier is by default not translatable.

Perhaps the scope of this issue is only the definition of the product category content type, which should have it's identifier attribute set as not translatable?