I had hoped to avoid getting into this brouhaha, but the more that I read, the more that I feel compelled to put in my two cents - which I'll do tonight.
Meanwhile, the short version is - I don't find the term Uniate offensive. What I do find offensive is rabid ranting that decries reality. Like it or not - there are ethnic Greek Catholics who worship according to the Byzantine Rite, few in number, but they exist. There are also Catholic Greeks - Latin Catholics who are ethnic Greeks, similarly few in number, but they exist too.
As to the use of the terminology in regards to other Eastern Catholics, not of the Byzantine Greek Catholic Church, it is of relatively recent origin, having tended to replace the usage "Byzantine" and used in its hyphenated form (Greek-Catholic), which it how it should appear, it's neither intended to be offensive nor should it be seen as an effort to lay claim to ethnicity and it sure as heck isn't going to fool anyone into thinking that the vast majority of us are Greek.
Frankly, the longer I consider it, the more I doubt the usefulness of this thread as the level of invective has effectively subjugated the question first posed.