You should not need an ID for renewal, OR for a first application, in fact. You may need to provide an ID to the Notary Public, if they do not personally know you.
Your decision on how to respond depends on how much trouble you are willing to endure. If you want to help the community, then you could give them only what is required by law, and then force them to deny your permit, and follow the process from there. If you don't want to take the time and trouble, then you will probably have to give them everything they ask for and they will continue to do it wrong.
I was able to successfully convince my local clerk on the ID requirement by walking them through the worst case scenario: What happens if John Doe submits Jim Smith's application? Nothing. The background check would be conducted on the name on the application, and the permit would still be mailed to the address on the application, and the person who possesses it would need to have a government issued photo ID in order to "use" it. Confirming the ID at the time of submission does not add anything to the process whatsoever.
ETA: By the way, THREE posts in almost FIVE years! That's some heavy duty lurking there!!