There are millions of US Citizens who hold the dual nationalities. It is perfectly normal in the USA since the USA is a country of migrants. People from all around the world migrated and settled in the USA. Nobody discriminates on the basis of your sex, color, origin or anything as far as you are US Citizen. However, rules regarding dual nationality are quite different in Saudi Arabia. Every country has a right to set the rules so I am not talking about the fairness or unfairness of those rules. The Saudi Government does not recognize the concept of dual nationality. (In this article I have used the example of US Citizen but you can apply it to your case even if you belong to some other country.
The Saudi government has confiscated the passport of US Citizens when they applied for the passport of Saudi Arabia several times. Confiscation of passport by Saudi Government does not mean that your US Citizenship is canceled; it has no impact on such activity. However, this act should be reported to the U.S. Embassy in Riyadh or the Consulates General in Jeddah or Dhahran. If you belong to some other nationality, you need to contact your embassy. It is very important for everyone to know that in the case of dual nationality, Saudi Arabia only recognizes the nationality of the documents used to enter to the KSA.
If a US citizen has a claim over Saudi Nationality, sometimes Saudi Embassy abroad issues Saudi Laissez Passer to him. I think the system will be same for other nationalities as well. I would never suggest you go to Saudi Arabia on Saudi Laissez Passer. You will be having a lot of trouble while coming back from KSA. They will require you to apply for the Saudi Nationality and Saudi Passport if you enter to Saudi Arabia on Saudi Laissez Passer. The procedure told by the Saudi Missions abroad to apply for the Saudi Nationality is expected to be largely difficult from the actual procedure. You would be very lucky if Saudi Nationality is bestowed upon you within 12 months of applying for it. In some cases, it takes 3, 4 years. Your US Passport will be confiscated by the government and you will be barred from traveling outside of Saudi Arabia unless a case of your nationality is finalized. Even if you take the passport from the government, you cannot fly out of Saudi Arabia since you entered to the Kingdom on Saudi Laissez Passer and not on US Passport. This is the reason, Saudi Government does not treat you US Citizen. So, I always suggest people enter to Saudi Arabia on US passport if you don’t have Saudi Passport.
However, if you have a passport of both nationalities USA and KSA, you should always use Saudi passport to enter to and go out from Kingdom of Saudi Arabia. However, Section 215 of the Immigration and Nationality Act (8 U.S.C. 1185) requires U.S. citizens to use a valid U.S. passport when entering or leaving the United States.
For further information on entry/exit requirements, travelers may contact the following Saudi government offices in the United States:
Royal Embassy of Saudi Arabia, 601 New Hampshire Ave., N.W., Washington, DC 20037, tel: (202) 342-3800.
Saudi Consulate General in Chicago: APTS 3106, 3109 & 3110, The Ritz Carlton Hotel, 160 East Pearson Street, Chicago, IL 60611, tel: (312) 560-8298.
Saudi Consulate General in Houston: 5718 Westheimer, Suite 1500, Houston, TX 77057, tel: (713) 785-5577.
Saudi Consulate General in Los Angeles: Sawtelle Courtyard Building, 2045 Sawtelle Blvd., Los Angeles, CA 90025, tel: (310) 479-6000.
Saudi Consulate General in New York: 866 United Nations Plaza, Suite 480, New York, NY 10017, tel: (212) 752-2740.