It does not make much sense to talk about royal "races" to me, other than "European" perhaps.

But if you look at it from a wide angel, they all are members of one large tribe of mixed Germanic origin I suppose. Even the Bourbons and the Savoys, as they all basically descend from the Germanic tribe leaders that overrun the Roman Empire :-D

Of course, with a few drops of local Celtic, Spanish, Italian, French, Hungarian and Slavic blood here and there!