Android has, or is soon to get, an incognito mode for the YouTube app, which will stop watched videos from showing up in your YouTube history. Google will still know exactly what you watch, of course. It’s just a way of keeping embarrassing movies out of your watched videos list.
iOS may or may not be getting the same feature, but that doesn’t matter. By using iOS’ (and the Mac’s) built-in tools, you can already watch YouTube videos without them showing up in your YouTube history. It even stops YouTube from tracking your history via cookies.