Frummy in the tummy, you may well be correct. Yale statistician Joseph Chang recently published a paper claiming that basically all of humanity is descended from every major historical figure. It may seem impossible, but (if I understand correctly) he claims that everyone of European ancestry is descended from Mohammed, and that virtually everyone in the world is descended from Egyptian pharaohs. If that’s true, we’re also all descendants of both Yaakov and Yishmael.
Think about it this way. Let’s say someone lived 1,000 years ago. That person had two descendants, and each of his descendants had an average of two descendants. Let’s say the average age of parenthood is 25. So that’s 40 generations. 2 to the power of 40 would be the number of his descendants. That number (one trillion) is many times larger than the present world population (about seven billion). This suggests that, for any person alive more than 1000 years ago, who has ancestors alive in the present day, most of humanity is that person’s descendant.
Although it may make sense mathematically, I think Chang’s argument doesn’t recognize that there are closed groups separated from the rest of humanity–to some extent Jews, even though a certain number of people have converted in every generation, but especially isolated indigenous peoples living in the Amazon rainforest or the New Guinea highlands.
Regardless, I think Chang’s work shows it doesn’t make sense to worry about who exactly is whose descendant. The approach cited above, to consider anyone living in an Arab country to be an Ishamaelite, makes the most sense.