I agree with your underlying argument, but I'm pretty sure "Coloured People" is a seriously offensive term to a large number (all?) of non-white people/people of colour.

I remember hearing that "people of colour" and "coloured people" are considered synonyms in many languages other than English and I'm assuming that's where you're coming from. They are not synonyms in English (especially not American English), even though the literal meaning is the same! The historical usage and connotations are very different, though I don't know this history well enough to explain it.

I understand the confusion: "People of colour" feels offensive to my Australian ears and it took me quite a while to get used to it's use online. Ah, language, getting in the way of communication for a hundred thousand years...