The countries that have a problem with Israeli stamps in passports have a problem with Israel (the country) or maybe Jewish people (the religious group).
The reason why they do is historic. In all due brevity, a Jewish nation has existed in areas that are now known as Israel in varying degrees of independence from 1000 BCE to around 100 or later CE. After Jews had left this area, they termed this diaspora and considered it a temporary phase before they could return to the same place again. In the meantime, the area was conquered by Arab and other muslim rulers who spent most of the second millenium CE in that part of the world. After the Second World War, a country for the Jewish people, Israel, was founded, which the muslim surrounding countries considered a breach of diplomatic standards and whatnot; therein lies the difficulties of the Israel–Palestine conflict.
Considering this, those countries that do not accept Israeli passports or passports containing Israeli stamps see both Jordan and Egypt ‘on their side’ — while both countries have noteable minorities of other religions, they are predominantly muslim. They are also both members of the Arab League, which also includes most countries that do not accept Israel.
Therefore, not visiting Israel but taking the ferry from Aqaba, Jordan, straight to Nuweiba, Egypt is their preferred way of going from one of those places to another. Any restrictions they have will be based on using the Aqaba–Eilat or Taba–Eilat border crossings.
And finally, even though anecdotic evidence is bad, I have briefly known somebody who travelled by bicycle through Jordan, took the ferry to Egypt, spent some time there, back to Jordan, back to Syria and onwards via Turkey to Iran and eastwards. She had no problems on that route, and Iran and Syria are two of the worst countries when it comes to Israeli passports or stamps. (This was in the first half of the 2000’s.)
