The arab/moor conquest and occupation of southern Europe brought in a lot a arab admixture into these countries, especially in the south. It was different from eastern europe somewhat in that there the invaders were driven back and out; whereas in Spain and Portugal the invaders occupied the lands for a significant amount of time. And Portugal brought back black slaves and eventually absorbed them into the population.
Also, with the Catholic Church demanding and accepting conversos, each country absorbed large numbers of jews into the populations. I read a recent genetic study of Spain that estimated 20% of the population today had jewish blood, whatever that is. My guess is that it would be much higher.
In the early 1500s, Erasmus, the Catholic humanist, commented that Spain at that time, was "crawling with jews," and he was talking about conversos--jews who had converted to Christianity. And he was making this comment more than 20 years after the general expulsion of the jews in 1492. There were so many converso jews in Spain that Erasmus refused to travel there.
The math is simple. Thousands of converso jews 600 years ago in Spain absorbed into the population. Given the size of Catholic families, that number would grow exponentially, spreading like wildfire through the population. And that's just the jews--when you add in the arab/moors, you can see how rapidly a population can be mongrelized.