Gold Card wants hukou renunciation proof, what to do for US citizen?

There was a case a while ago on this forum of a foreigner born in China to foreign parents, hence he never had PRC citizenship, left China, and Taiwan wanted him to provide proof of renunciation. In his case, it’s impossible to get any documentation since he was never a PRC citizen.

Another option is you could call NIA and ask to appeal to their supervisor / head of NIA.