NEW YORK — He was “America’s Mayor” but never an American Idol. Rudy Giuliani was shockingly unmasked at a taping of Fox’s “The Masked Singer” last week, sparking judges Ken Jeong and Robin Thicke to walk off the set in protest, according to multiple reports. The show recently began filming its seventh season, but Giuliani was unable to flex the golden pipes and was the first contestant eliminated, Deadline reported. Jeong and Thicke, reportedly furious, stormed off set, according to TMZ. They eventually returned. The other two judges, Jenny McCarthy and Nicole Scherzinger, didn’t go anywhere,…