Shah Reza Pahlavi did propose to a European Catholic royal, but I can't remember who or where from. He also proposed to Grace Kelly. Either way, both rejected him.
I can't really see European royal families or even noble families inter-marrying non-European (or non-European-American) royals. Racism is too rampant, and the majority of European royals would look down upon mixed-raced children.
This said, I think Prince Joachim of Denmark, second inline to the throne, had two children with his first wife, who was of partial Chinese origin.
Racism eventually, from both sides, but earlier on I think the biggest barrier would be cultural and religious.
I think you'd need (1) a religiously compatible marriage and (2) some kind of financial or military benefit to it.