For Star Trek. I don't mind.
This is a fictional universe taking place hundreds of years in the future. After a World War that has obliterated a decent chunk of civilization, contact with aliens, and quick and near ubiqitous travel.
Over time I would imagine ethnic breakdowns of countries and entire regions could be radically different than they are now in only a few years time.
Intermarriage and old prejudices dying away, and it being no big deal to pick up and move to another planet, much less another country. No reason a Brit couldn't be French. No reason there couldn't be a sizable Japanese population in China. Heck, I think there is little info that certain countries even exist anymore.
So, basically. I don't let it bother me. Maybe if a series was taking place a little closer to now, like right after First Contact. But in the 23rd/24th centuries.