Even "Euromutts" are usually only mixed within a small range of related people. It's like, I doubt that you're Igbo, Ainu, Peruvian and Norwegian. "Supermixed" people like Wentworth Miller (and, I suppose, me to a lesser extent) are a rarity in this world.
"Euro" means "Europe". I might have one or two ancestors from those non-European peoples, but it's not likely to be very significant.
However, having largely Irish ancestry automatically means likely having a significant Danish/Norwegian ancestry going back to Viking times. I also have English ancestry since my Irish great-great-grandmother married while in the US, someone who was descended from an English noble house. That means I have Welsh, Cornish, Saxon, probably Friis and Angle, Norman, and more Danish/Norwegian Viking at that time. I also have significant Greek ancestry, which could mean pretty much anything including having significant Roman, Turkish, and Persian ancestry when going back far enough.
That's why I feel it's a silly thing to worry about these things.
Except that race exists. I used to deny it, too, until I considered the biological data. There are variations within the human species and one expression of this are the different races. That's just scientific fact. It's what this means that it is up for debate. But it's not as simple as saying "white people", "black people", Asians", etc. The various groups within those monolithic concepts are where the real divisions come into play. Even in Europe, with its history of conquests and migrations, there is still a considerable phenotypical diversity. Not as much as Africa, of course, but still noteworthy.
But that's an entirely different matter, and I wouldn't label it as "race". Due to all the upheaval that began with Rome and then later the Migration Age, it basically means all of Europe's peoples are mutliracial.
You're ignoring that most of the European peoples have a common Indo-European root
Culturally and linguistically, not necessarily ethnically.
as it is and, to my knowledge, have never undergone such large scale non-European immigration except for things like the Islamic conquests (ooh, irony). What I'm talking about is white Europeans being gradually replaced by Arabs, Pakistanis and North Africans. I highly doubt they're going to care very much for Indo-European civilization, if it does indeed get to that point. I can't think of one example where a group replaced another group in an area and continued the former group's civilization.
I can think of four off the top of my head: France, Ireland, Russia, Egypt. I'd wager there's more.
However, I can only think of a single instance of an entire ethnic group being replaced by another: that of Europeans replacing the natives of North America. The reason there has nothing to do with the invasion directly, but because of the smallpox plague reducing the population so much that it was, in every way, apocalyptic. Makes the Black Death look like the annual flu. The USA is literally built on the remains of post-apocalyptia.
"Indo-European civilization" is a new one on me. I've never heard of such a thing.