We should work to change that.
Perhaps we should first assess reality of ciero’s comment. Right off the bat, one thing that can be said is how relatively and exceedingly rare are the occasions in which we see Ruthenians complaining about the activities of other particular churches.
It is, of course, true, that in the early days in this country, there was division between the Ukrainians and “us”. In fact this division was already consolidated within brotherhoods decades before it was reflected in separate jurisdictions with different bishops. That is regrettable to some extent, but the Ukrainians had a clear poltical-ethnic, which to their credit, helped eventually lead to the formation of Ukrainian nation. We were not part of that, and, in fact, our own sense of national identity was murky. That separation may have been inevitable, at that time. Does it lingering effects? Perhaps. It would be great to work better together.
What of our use of “Byzantine”? In the old country we were Greek Catholics. That led, genuinely, to confusion with ethnic Greeks here. The shift to “Byzantine” was made. Was there a hue an cry about this shift from others who use the Byzantine rite? Maybe, but I haven’t seen or heard any such complaints until very recently. And I see Russians, Romanians, and others shifting to this usage too. I have not heard of any multilateral discussions on this new usage, nor any complaint about it whatsoever. IMO, this complaint is a red herring.
Was this shift connected to forging an American identity? Probably not. “Byzantine” is not exactly American. I think that any church could and should choose to highlight their ethnic origins however they like. I cannot see why this should be a multilateral affair. I am happy for this rather sensitive matter to be handled by each particular church. And I certainly do not begrudge efforts by bishops in particular churches to handle this matter, or to regulate the manner in which divine services are conducted under them; that is what bishops do.
Even so, there is room for cooperation. We have offered our temples for the use of mission parishes for Melkites, Romanians, and various EO and OO churches. I don’t know if that cooperation has been reciprocated, and I don’t especially care - apart from forging a reality-based understanding of the notion of not playing well with others. Our seminary is and has been utilized in the formation of Romanian, Melkite, Slovak (Canada and Slovakia), and Ukrainian priests; we have a Melkite and several Orthodox priests on the faculty. Our bishops have been elected as leaders of the Conference of Eastern Catholic Bishops.
Is there room for furthering these relationships. Of course. Primarily I would love to see more cooperation - much more cooperation - in the establishing of missions. There have been situations even of late that are very messy; such messes should be avoided, scrupulously.
One thing that will help in furthering these relationships - arguably a sine qua non of furthering them - is mutual respect.