They were conquered and lived in dhimmitude for quite a while. Just practice your manners and you'll be fine.
The people in the far North were not conquered.
The Reconquista was initiated by King San Cho Noe I who came from Cornwall and landed in Galicia. He and his people founded three kingdoms ~ Leon, Castile and Carvajal.
Together these three kingdoms served to conquer all of Spain and eventually displace Islamic authority.
Once that was done under Isabella and Ferdinand, they set their eyes to the West and conquered half a world.
Dhimmitude? You jest!