Letters of Recommendation requests
I don't know what the "company's registrar auditor" is. Perhaps I am missing something, but, in general, I don't see why it might be unethical for you to ask somebody for a reference. One can imagine circumstances under which one might be seeking a reference where a conflict of interest is involved, e.g., getting this from a cousin. But even in that case, it would be all right if the cousin did not conceal the relationship. It would be up to the cousin to behave properly.
I suspect there may be a more interesting ethics issue related to a "Quality Manager" (I assume this means quality control manager) feeling the need to resign, presumably in protest against some company action or policy.