Well, knowing the Ukrainians very well (my own mother’s family comes from just north of there, from Belarus), they are fiercely proud of their heritage, and there’s nothing wrong with that, if it doesn’t get in the way of their faith.
The ethnicity issue is different in Orthodoxy than it is in Catholicism, and the reason is ecclesiological. It is certainly true that Eastern Catholicism can be very ethnic. For that matter Latin Rite can have a heavily ethnic flavor (Irish, Italian, Polish, Latino, etc.). The difference, imo, is that Catholics are Catholic first, and they share “communio in sacris”, so that whatever multiplicity of surface differences there may be, Eastern or Western, Byzantine Liturgy, Latin Mass or Novus Ordo, the faithful are united by the Eucharist and and the pastoral oversight of the Holy See on moral and dogmatic issues. The Catholic Church may be plagued with problems of it’s own, but it seems to have captured universality more successfully.
The problem with Orthodoxy is that, historically speaking, each jurisdiction is tied to the Mother Church of the respective Mother Country. And, also historically speaking, all of those mother countries happen to be “eastern”. So an organic, historical “western” expression of Orthodoxy cannot and does not exist. There is a floundering Western Rite that is a 20th century reconstruction of pre-schism proto-Catholicism, but it’s small, and it’s regarded with scorn and suspicion. Generally, “western” in Orthodoxy means one thing, “heretical”. That means, practically speaking, that you can’t be western and be Orthodox. You have to learn to be Greek or Russian, etc. before you can practice the faith. And, more importantly, you have no idea who’s in charge of what, where the Church stands on social or moral issues, etc., and if (God forbid) there should be pastoral misconduct of any sort (financial, sexual, etc.), there is no clear line of accountability and no “processibus” to handle the problem.
This is what makes Orthodoxy’s ethnicity problem unique, imo.