Is it illegal to make moonshine in a US state?

Yes, because it's a violation of federal law. Even if state law permits it, it's still a federal crime.

Note that licensed distillers can produce a product identical in every way to the illegal home-distilled product except that it was produced by a licensed distillery (and that taxes were properly paid on it), and even call it "Moonshine" if they like, and that's perfectly legal. But distillation of alcohol by anyone but a licensed distiller is illegal, and licenses are essentially never given for home/hobby distillation.