I am a learner here…
I equate Orthodoxy, beyond some basic theological issues, as being primarily that of ethnicicfty.
As a north American, I suppose that would your first concern.
Ethnicity was once, in the nineteenth century, a serious problem for the Latin Catholic church in America as well, and it discouraged conversion of the ‘native’ WASP population. This is why the American Catholic bishops embraced ‘Americanism’ (something that was condemned by the Pope), they desired to present a more favorable “American” image to the general mostly non-Catholic American public.
Over time this has become less of an issue, except perhaps in the case of large scale recent immigration of Spanish speaking people, because the earlier populations of Irish, Germans, Poles and Italians have largely assimilated into the north American culture and there is now an “American” ethnicity which dominates in the “American” Catholic church.
Holy Orthodoxy, which began to grow early in the twentieth century, is going through the same process of assimilation, but is perhaps fifty to seventy-five years behind the Roman Catholics. Today one can find most parishes use English and have a mixed ethnicity, despite the name of the synod being from some country abroad.
The case of the Ethiopian church is interesting. It probably should not be called a “uniate” church because it is not Orthodox, but Miaphysite. The story is instructive though.
The Portuguese Jesuits arrived in Ethiopia and required the king to submit to the Pope as a condition for military aid! This happened in 1624AD. By 1633AD the Jesuits (whom had already alienated the population) were forcibly expelled and their books were burned.
The modern Ethiopian Catholic church is a result of later Catholic missions when Europe was carving up Africa and the country was weak. The missions at first targeted the Ethiopean Christians (not, as it were, the Muslims and Pagans) in order to ‘poach’ them away from their native church.
Later, a missioner named de Jacobis got the bright idea that he would have more success in winning away the Ethiopian Christians by imitating the native Ethiopian church in it’s liturgical practices and vestments, so that is what he did. He was opposed by some in the Curia for this but did meet with much greater success. He was later canonized for this successful policy of poaching.
Thus, the modern Ethiopian
Catholic church is not the result of the historic native Ethiopian Orthodox seeking union with Rome, but is a new church founded in the nineteenth century by European missioners.
It also happens to be the only case I know of today where an “Eastern Catholic” church actually has two rites (Latin and Coptic), with some Latin Catholic bishops, priests and laity under it’s Metropolitan. Both rites began in Ethiopia as nineteenth century missions, the Latin rite presumably got a big boost when Italy attacked and occupied the country.