I'm a bit confused on this issue myself. I am currently under moderation for using a certain term which I was unaware is not allowed here (hence, I completely accept the moderation, and am not meaning this post as a challenge to the moderators...just FYI
), but which has been historically used without prejudice by the Roman Church itself to refer to its Eastern compatriots for centuries, and only recently acquired a supposedly-pejorative meaning. That in itself is odd to me, because you know what also had a pejorative meaning, originally? "Roman Catholic", when it was being used by Protestants to smear the adherents of Rome in Europe during the Reformation! And yet you hardly ever see self-described Roman Catholics saying that this is inappropriate.
So for someone outside of that communion, even if they want to use the right term it can be hard to know in advance what should be used, because you cab have a term that one group uses proudly as a descriptor but another group of the same communion thinks is a horrible offense and should never be used. I realize that rites are not churches, but there are enough examples within the Roman communion of a church being established from a section of a much older Orthodox church, thereby making the rite that they bring with them (or whatever modification thereof that they use) unique to that church, that I think this particular error should be forgiven. In some cases, the new Rome-affiliated churches even come with newly minted ethnicities or at least ethnoreligious identities (e.g., Chaldean, Maronite), making the situation even more confusing for the outsider.