Answer (first posted by @lawyerdad ): I think the idea is that with any clothes, if you turn the them inside out you add a slight bit of protection against the outside surface getting abraded or whatever by the insides of the machinery. For people who are super focused on fades, turning jeans inside out probably doesn't hurt anything and theoretically may prevent having some uneven indigo loss where the jeans rub up against the machinery. But it's not like your jeans are waterproof. The soapy water's going to get to both sides either way.
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