My former organization had a strict dress code, for lack of a better phrase. Black belts wore their belt with the organization’s kanji on the left side, and the person’s name in kanji and stripes on the right side. The head of that organization is a Vietnam vet and spent quite some time in the Marine Corps, so uniform actually meant uniform. Kyu ranks got electrical tape stripes and they were supposed to be worn on the right, but that wasn’t enforced, surprisingly even by the head guy. He’d make a comment every now and then, but he wouldn’t go crazy with it like other things.
My current organization doesn’t care which side stripes are on. My teacher gets asked this one occasionally, and he says he’s asked several times with no definitive answer. He looks at our founder and his son who is his official successor, and both wear them opposite of each other. He watches when Kaicho ties a black belt on people after they’ve been promoted, and it’s whatever side it ends up on. The only universal thing is have the embroidered side out instead of the underside.