I personally wish the same stringent law of domain d'origine was applied here. We can't call Australian sparkling wine made on Pinot noir grapes champagne. If it didn't come out of a cow, sheep, goat, or in the case of "red dwarf" dog teat, I don't think it should be called milk or even mylk.

Partner of a nut anaphylaxis sufferer, parent of a formerly cow milk intolerant child so I've straddled both sides of what people need in their life. The answer imnsho is clarity: call it what it is specifically. (Which most people here do. Nut milk. Oat milk. Soy milk) but please, don't call it milk, unqualified.