the arabs tried to invade italy repeatedly, but constructing racial arguments around it is anachronistic. the revisionism is not in rejecting the racial narrative, but in constructing it.
the empire was not a roman concept, it was a persian one. the king of kings was the persian emperor. the empire had a kind of feudal structure beneath, where rulers of client states like armenia could refer to themselves as kings, so long as they accepted the king of kings - the persian emperor. when alexander broke persian power, he left a series of weak states that ended up warring with each other. the seleucids often styled themselves king-of-kings but it was never in reality. as the hellenic period fell apart, random despots started using the title - much as random despots today use the term caliph (itself a conceptual descendant of the persian hegemony). a part of the reason that the romans were able to absorb the levant so easily is that they were looking for a stable overlord, and entrance in a stable empire. in half of the persian lands, the roman emperor became the king-of-kings - but the persians never liked this much, and they fought for a thousand years over who got to be the true hegemon.
but, all of this fighting between rome and persia for hegemony over the middle east just recreated the same problem that existed at the end of hellenism. the people wanted a stable empire to exist within, so that they could trade and drink wine and carry out their rituals. islam was maybe not what they asked for, but it was at least a unifying force. and, so, the caliph became the king of kings and the emperor must be forced to submit.
in fact, it is the emperor's refusal to submit that is unique in history. the greeks conquered the persians, and the romans conquered the greeks. the arabs were not able to fully conquer the romans. and, so, what was one civilization broke apart into two.
so, when the arabs were carrying out months or years long seiges on constantinople, and launching their thirteenth invasion of italy or whatever it was, they weren't seeing it as invading a foreign land. to them, they were completing their conquest of the single empire that had always existed.
and, likewise, the crusaders did not see themselves as stealing land from arabs, but as taking what was rightfully theirs - because there was no concept of christianity and islam as separate cultures, but only of a broader western culture seized by civil war.
the consensus amongst roman historians for the first century or so of islam was actually that it was what was called a heresy, which is a very technical term, in context. muslims weren't seen as a different religion, but merely as confused christians that had deviated from orthodoxy.
centuries later, the turkish sultan was still insisting on calling himself not just the caliph, but also the roman emperor and, still, the king-of-kings - as these were all one and the same thing. and, this idea of christians and muslims as culturally separate is really a consequence of the renaissance.