Am I correct in assuming that “Basque” has a Muslim connotation?
There are so many variations of people and their heritage.
The Muslims in Michagan have joined our American parents in the scandals in the American schools.
The Basques are the weirdest people in Europe, with obscure but ancient origins and a language unrelated to any other anywhere. We even have peculiar physical/genetic characteristics.
https://en.m.wikipedia.org/wiki/Basques
As for Muslims, the Basques (and the Galicians/Asturians/Catalans. Everyone in the north says that) were reputed to be the last holdouts against the Muslims, and whence the reconquista began. This is not entirely true, but mostly so. All the Castillian noble houses are descended from Basque ancestors or so was their boast. And that is also true, if tenuous.
Therefore, in medieval times, the Crown of Castile traditionally conceded the status of “hidalguia”, that is, being a hidalgo, or member of the gentry, to all Basques, however humble, due to their supposed purity of blood, having never been Muslim. It was however only valid within the Basque country. But of course everyone obtained a coat of arms, and you will find all sorts of them carved over farmhouse doorways, stone posts on sheep pens, crypts, et cetera.