Traveling to Saudi Arabia from Israel
#1 Where is the other passport from?
#2 I know that US citizens or almost any other passport holder have to get a visa from embassy prior to a visit.
I know that if Saudi sees any Israeli stamp on any Passport they will deny entry.
I also have 2 passports and on my third visit for Umrah they searched carry on and found other passport and flipped thru all pages.
#3 If they search your belongings and find other passport with Israeli stamp they will hold you and question you even more.
Good luck