Earlier quoted context omitted.
I'm not so sure. Even with modern transportation technologies, the price of moving is still high enough that the number of single ethnicity births will generally outpace multi-ethnicity births. I don't think we have nearly enough airplanes and jet fuel to homogenize the genetics of ~8 billion people. But I also haven't run those numbers so feel free to change my mind.
A few instances of "new blood" in a population can be enough because it will then spread over generations. In many countries the proportion of foreign-born is >10%, so the mixing is quite intense in terms of evolutionary time scales. If that continues for a few hundreds of years, diversity will have significantly reduced. Indeed, some suggest that e.g. skin colour may largely homogenise within a thousand years. A tho…
The last X is an easy target.
on edit: for anyone unfamiliar with this trope, see https://en.wikipedia.org/wiki/Requiem_for_Methuselah or https://en.wikipedia.org/wiki/The_Man_from_Earth (both written by Jerome Bixby, but many other examples by Neil Gaiman, etc. available) for easy clarification. One of the common ideas of the trope is that an immortal sooner or later becomes problematic to have in one place, they must wander of people will attempt to experiment on them to figure out the secret of immortality. Of course the second bit of the trope is the wandering immortal leave traces, and more intense searchers after immortality will follow them and attempt capture. If diversity decreases in the future based on present trends the story then becomes that it becomes increasingly difficult for the wandering immortal to wander without everyone being aware of them.