There's also the small matter of the Hessian mercenaries used in the Texan War of Independence. It seems that some of Santa Ana's soldier's, being good Catholics, had a bit of problem with killing Mexican, Spanish, and Irish Catholics on the Texan side. To get around this, he hired the Hessians, who , being Protestant, had no problem killing Catholics. They also had plenty of practice at it as well.
After the Texans beat the Mexican army, some of the Hessians settled in Mexico City, among other places. This not only explains the Germanic influences on the music, but also the fact that there are blond-haired, blue-eyed Mexicans.