I'm not coming to this as a historian as such, but I think clarification would help. Do you mean intermarriage between the Egyptian people, or do you mean within the families of the leaders - and are we talking any specific dynasty of pharoahs?

But simply put, it takes a number of generations of incestuous breeding to really have a marked increase in the risk of the child being born with some sort of issue - for the first few generations the risk is barely more than it is compared to less closely related parents. And on top of that, if the parents create two or more children that survive to breed, then the family line is sustained - it takes two to make two, and those two can make two, and so on. Two children is not, generally speaking, a great feat for a set of parents to create.

But there's also the idea that not all children were born of these pairings. It's put forward by Stacy Schiff in Cleopatra: A Life that, as an example, Cleopatra wouldn't have engaged in sexual relations with any of her husbands (and it's likely she had sex with two or three people at most, the third being Caesarion's suspected real father - suspected because Caesar had no issue through his notorious sleeping around nor by his wives, ergo Caesarion's father is plausibly not Caesar) despite the marriage. Cleopatra herself is not of a sibling union, but one where her father was both uncle and cousin to her mother.