U.S. policy on dual nationality can be found
CIA World Factbook reports: "Western Sahara is a non-self-governing territory...Morocco annexed the northern two-thirds of Western Sahara and claimed the rest of the territory in 1979...A guerrilla war with the Polisario Front contesting Morocco`s sovereignty ended in a 1991 cease-fire and the establishment of a UN peacekeeping operation. As part of this effort, the UN sought to offer a choice to the peoples of Western Sahara between independence (favored by the Polisario Front) or integration into Morocco. A proposed referendum on the question of independence never took place due to lack of agreement on voter eligibility. The approximately 1,600 km- (almost 1,000 mi-) long defensive sand berm, built by the Moroccans from 1980 to 1987 and running the length of the territory, continues to separate the opposing forces, with Morocco controlling the roughly three-quarters of the territory west of the berm. There are periodic ethnic tensions between the native Sahrawi population and Moroccan immigrants. Morocco maintains a heavy security presence in the territory. The UN revived direct talks between the two parties to the conflict - Morocco and the Polisario Front - in December 2018."
Wikitravel explains: "The vast majority of Western Sahara is administered by Morocco, which considers it an integral part of its territory, so the same entry conditions apply as for Morocco itself. However, independent travel in the region is restricted, and while crossing through Western Sahara while travelling overland between Morocco and Mauritania is usually OK, some travellers have been turned back when trying to enter, especially during periods of political strife."
GOV.UK confirms: "Travel is restricted and while organised groups are generally permitted, independent travellers should be aware that they could be turned back at the border...Make sure your passport is stamped when you enter the territory. Some tourists have experienced difficulties leaving the country because their passports had no entry stamp."
Rough Guide details: "Tourists can travel freely in most Moroccan-controlled parts...but do check first on the political situation. 2010 and 2011 saw violent clashes between Saharawis and Moroccan settlers and police in Laayoune, Smara and Dakhla, among other places, and you should be aware that protests often involve violence, and should be avoided...Apart from this, the only obstacle would be for visitors who admit to being a writer or journalist: a profession not welcome in the region, unless under the aegis of an official press tour. Otherwise, visiting Laayoune, Smara, Boujdour and Dakhla is now pretty routine, though it does involve answering a series of questions (name, age, profession, parents’ names, passport number and date of issue etc) at numerous police checkpoints along the way. This is all usually very amicable, but time-consuming..."
Regarding the area of Western Sahara not controlled by Morocco (called "SADR-contolled"), Wikitravel reports: "Official entry requirements for SADR-controlled areas are unclear, but in practice the area is entirely off-limits to visitors: you cannot legally cross the heavily guarded and mined Berm from the Moroccan-controlled side, the land border with Algeria is closed, and there are no legal border crossings from Mauritania into SADR-controlled territory either."