As a general rule we may say that the fact of having stamps from Arabic or Muslim countries in a passport when one is entering Israel should not represent a problem. But this is just the general rule.
Security measures when crossing Ben Gurion airport are quite tight. It actually starts even before boarding a plane with Israel as a destination. Whomever will fly there must keep this in mind and the ideal thing is not having many stamps from Arabic or Middle Eastern countries in one passport. Most countries understand the problem that this can represent and they are willing to provide a new passport for the traveler to Israel.
Just landing in Tel Aviv the tight security is evident, and this is even tighter if one is flying in one of the very few flights from a Muslim country such as Turkish or Royal Jordanian.
Along the airport it is normal to see police agents who randomly choose passengers to check their passports and ask several questions. The important thing is to keep calm and answer honestly, and should not be any problem.
Exiting Israel one has to go again through very strict security. Many times those with Arabic stamps will get a harder time when leaving. When one is in line for check-in, security agents check the passports and they assign a color for those they think need to go through a more extended scanning process. Our experience is that those with stamps from Arabic countries are always required to go trough extra screening. Once again the most important thing is to keep calm, answer straight and honestly and be open to an extra revision of the luggage.
Some members of our team with several stamps from Egypt, UAE, Jordan and Indonesia have gone through Ben Gurion airport in Tel Aviv, they always have experienced questioning or the extra screening, but besides of that they never have had any other problem.
We have been receiving some updates about this topic, and the situation continues being more or less the same, but travelers with stamps in their passports from Middle Eastern countries have been experiencing some extra questioning and luggage screening, what is interesting is that most travelers have been experiencing that not on their arrival, but before departure, but so far we have not heard of any particular case of someone who has been denied to board because of that.