Bumbling American comments:
From the Catholic side of things: The sense I get from the pulpit and the Vatican is that Euro/American Catholics are being preached *at*, while the Global South is being preached *to*. We (the Euro/Americans) must welcome, we most accommodate, we must change to meet the new realities, etc. Whereas the Global Southerners are, by implication, sacralized as the transmitters of those new realities. There's no call for reciprocal respect or understanding, let alone forbearance about moving to somebody else's homeland and disrupting it in a dozen ways. We're all one big happy ecclesiastical family, but some of the drunken cousins get more slack than everybody else.
From the Orthodox side, here is my perspective:
For two centuries, the Orthodox Church in America viewed herself as a diaspora Church, even though no such thing has ever existed in Church history. Now that the prior waves of immigration have dried up and subsequent generations have outmarried, all the aging Greeks, Slavs and Middle Easterners suddenly realize they cannot pay the bills by continuing to be diaspora parishes. Even the Greek Cathedral in my hometown puts up a "Come and see!" banner at its annual festival. Hilariously, after two centuries in this country the Greek Archdiocese has decided to evangelize ... Hispanics. If you dig around a bit, you can also find the nascent Mayan Orthodoxy, which proudly proclaims, "The story of a native Church." When Heimbach and his pals agitate for the same thing for American whites, it is apparently an excommunicable sin.
Everywhere but in the American nation-state, people are to be allowed their Blut und Boden. (Of course, Arab Christian loyalty to their homelands is repaid with the equally ardent Muslim desire to extinguish Arab Christians and their Shia allies from the reformed Umayyad. This is the fault, I have been personally told by Arab Christian refugees, of Americans and Jews.)
The multicultural flavor of the Antiochian patriarchate is undeniable, and there is a lot of trumpeting of our archdiocese as the "genuine" Orthodox branch for a propositional nation like the US. But there is only so far out on that diversity limb that people can politely go. Diversity is, in modern parlance, great and all, but nobody wants to think too hard about where diversity comes from. The idea that distinctive nations emerged from tribes drawing lines around themselves and marrying each other's daughters to insure they remained the dominant ethnicity violates a lot of narratives. People would rather imagine that the storks got together and decided to drop all Greek, Russian, Jewish, African, Finnish and Persian babies on different days.
Orthodoxy in America has a strongly juvenile (i.e, present-oriented, American) flavor in that for only the past generation has it become a redoubt for higher-g adult converts, like the Church in Jerusalem on the day of Pentecost, 33 A.D.
Pentecost, it seems to me, is where most American Orthodox would like the Church in the US to stay: a permanently juvenescent movement relying on growth, if it occurs at all, from adult conversions. In Orthodox homelands of course, the Local Church is woven into the national fabric. You are Churched and baptized into the Faith from your earliest memory. Nobody wrings their hands over what church to "join." That decision was made for you when you were baptized. (Sacramental baptism is another one of those things American Orthodox don't really seem to grasp.) The church is simply the Church, as it is in Serbia, Bulgaria, Russia, Greece, or in Roman Catholic Croatia, Poland, Italy, Ireland and elsewhere. Americans pride themselves on being above such narrow provincialism, and the end result is 300+ million deracinated, atheistic, exhausted strangers for whom religious worship is entirely a matter of ideological preference.
I am coming to the conclusion that America so long as it is not an actual nation will never have an actual Church. I sometimes wonder if the utter silence of the mother Churches on the uncanonical situation in the Americas and elsewhere is just their cynical determination to wait things out, and see what nations emerge after it all ends in tears.
UPDATE: It occurs to me that if Matthew Heimbach has been excommunicated for phyletism, then all our American Orthodox hierarchs need to disqualify themselves from serving. Don't we have a Great and Holy Council coming up? Isn't the fact that the entire Church in America is uncanonical kind of important? Or do they view the US Church as more just a funding vehicle for the real Church back home?