The Empire of Oil is one of the major number bloodlines. It includes descendents of both Crusaders and their apparent enemies, the Knights of Islam. Of course both during the Middle Ages when the Crusades took place and subsequently, defining friends and enemies is not as easy a task as may first appear.
If we consider that the "enemy" is that group on whom we deliver the greatest damage, then both during the time of the Crusades and now some of the major enemies of the Empire of Oil are the urban and rural poor and people of the Jewish faith. Hundreds of thousands of poor people and tens of thousands of Jewish people were exterminated during the Crusades at the same time as leaders of the armies were far more frequently accorded great respect by their "enemies"- presumably due to them all being members of the same global elite. Much as is the case today. Only those members of the elite whose elevation is seen as illegitimate, or who buck the system and tell the truth in some way to the public- usually end up publically executed.
A related question is how one defines the Middle Ages at all in the first place.
I would suggest that a practical definition might turn more on the beginning of the Crusades and the associated mass media control of Europe by the Catholic Church rather than some pointless timeline based attempt to define an emergent Medieval culture. Only the Crusades provided the strong demarcation between what came before and how Europe changed afterwards.
The First Crusade, like 9/11... "changed everything"...