In Canada, "Eskimo" has been rarely used for a good thirty years or so, if not longer, among educated people, at least. It is a name given the Inuit by their Native (Indian) enemies, and apparently means "eaters of raw meat". Which they are, of course - however, it is a custom which has been used to mock them, and I think that is the basis of whatever sensitivity they or some of them have regarding the term "Eskimo". Apart from the fact that it is simply not what they call themselves in their own language (Inuttitut), which is still widely spoken.

In the Inuit village in which I spent several years, the young people used the term "Eskimo" to refer jocularly to what they seemed to consider their pre-modern ancestors and their culture - "pre-modern", in their case, meant pre-1960s. The kids seemed both proud of and amused by their rugged forebears; they clearly saw themselves as connected with but culturally different from "Eskimos".

By the way, they would get a kick out of hearing someone referred to as "white" - "How white was he?" was a typical response. Don't know what they would have made of "Caucasian". But I can imagine ...

As to who decided that "Eskimo" had "suddenly" become demeaning, etc. - well, the push to replace the usage no doubt came out of some university. But - I think you might find it easier just to accept changing fashions in usage; there's not much you can do about it.