I will reword and answer the question as, "How well accepted were the Hashemite Kings in that the British imposed on Transjordan and Iraq after World War I?" Because the answers are rather different.
The current king of "Jordan" is Abdullah II. He is the son of the late (and popular) King Hussein. Hussein was the grandson of Abdullah I, one of the two ...
During that time, Pan-Arabism was in fashion in the Arabic world. The lineage of these rulers going back to the clan of the prophet Mohamed of Islam was a plus.
Arab countries were trying to unite in several competing failed projects. Where you come from was not as important as to what political dogma you had.