In addition to the two threads posted by /u/Agent_85 which point to contrary evidence from antiquity, the weirdest part of this to me is that the Arab invasions somehow carried out this whitewashing (pun fully intended of history.
Because it's incumbent on someone putting forth such a theory to provide evidence for it, here are some things I would want to know:
- Why would the Arabs have done this? What motive would they have had? Who would have given the order?
- When did the Arabs do this? Under the reign of some particular Caliph? All of them? Assuming it took many years, how do explain the dedication of Caliphal policy, including across competing dynasties, towards such a strangely Quixotic goal?
- Why did the Arabs not write about this?
- Why did the occupants of Christian Egypt not write about them doing this?
- Why did the people who fled Egypt to go to unoccupied Byzantine territory not write about this?
- Why did no previous Byzantine Egyptian write about this?
- Why, when in many ways the Arab Muslims were incredibly open-minded about race and ethnicity, would they have found black rule of Egypt to be uniquely offensive and in need of erasure?
- Where were these statue nose removals taking place? Were the Arabs running around with archaeological expeditions that would dig up a statue, break a nose, and then put it back in the sand?
- How does this tie in with the actual recorded understanding of what the Arabs thought ancient Egyptian civilization was, namely, the Pyramids were built by an anti-diluvian (i.e. before Noah's flood) set of pre-biblical kings?
- Why just the noses? There is certainly enough of a tradition in Islam of iconoclasm that surely if they had such a policy in mind they could have just destroyed the statues in their entirety.
That's just a few of the obvious problems I see about this theory. I could probably go on, but the basic answer is that this idea is utter nonsense.