Islamic law generally forbids men from touching women to whom they are not related. However, that rule is often times overlooked when official diplomatic delegations visit the kingdom.
The White House notes that representatives of the United States, including former Secretaries of State Hillary Clinton and Madeleine Albright, along with German Chancellor Angela Merkel have all visited the Saudi king, and have all shaken hands with members of the Saudi royal family.
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Islamic experts also point to another central theme of Islam: hospitality. When one is a guest in someone's home, they are treated as family.
Obama also did not cover her head, eschewing strict religious and cultural customs in Saudi Arabia, where women wear a full-body garment called an abaya and cover their heads with a hijab or the more conservative niqab, which has only a slit for the eyes.
Obama's predecessor Laura Bush also did not cover her head during her 2007 solo visit to Saudi Arabia and neither did Hillary Clinton during a 2010 trip to the kingdom as Secretary of State. Another former secretary of state, Condoleeza Rice, also did not cover her head as she joined the U.S. delegation in Saudi Arabia on Tuesday.
But the U.S. State Department advises other American women visiting the country that they could face problems if they don't cover their heads.
"Women who choose not to conform to this dress code face a risk of confrontation by Mutawwa (religious police) and possible detention/arrest," the State Department says on its website. "While most incidents have resulted only in inconvenience or embarrassment, the potential exists for an individual to be arrested, physically harmed, or deported."
Additionally, female tourists who don't abide by the dress code or sidestep other religious laws -- like walking in public unaccompanied or mingling with men who aren't relatives -- risk being harassed, pursued or assaulted by Saudi citizens, the State Department warns.
Pool reporters traveling with the President on Air Force One, also pointed out that in the receiving line at the airport in Saudi Arabia - a more open setting than the palace -- Michelle Obama stood next to but slightly behind the President, and held a small black clutch purse in front of her with both hands.
Reporters say they noticed that Mrs. Obama waited for a gesture to be made to her by the men who walked by, and if the man initiated a handshake, she smiled and shook their hand. If not, both she and the man politely smiled and nodded heads.
Perceived problems of etiquette have come up before with the first lady. In 2009 during her first meeting with Queen Elizabeth in Britain, she drew headlines when she hugged the monarch. British tabloids picked up on the embrace, and some noted that etiquette wasn't followed, because people aren't supposed to touch the queen. However, other outlets quickly noted that the queen returned the hug.
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President Obama has had his fair share of criticism as well. Critics took issue when he bowed in front of Saudi King Abdullah at a G20 meeting in 2009, and again for bowing to the Japanese Emperor Akihito. Although, aides at the time told CNN on condition of anonymity that, "It wasn't a bow. He grasped his hand with two hands, and he's taller than King Abdullah."
Former Vice President Dick Cheney was one of Obama's most vocal critics and said an American leader should never bow to anyone. However, a State Department spokesperson at the time told CNN that, "It's a natural response of the President the first time he meets the Japanese head of state, to show a sign of respect."
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CNN's Jeremy Diamond contributed to this report.