On December 11, 2015, President Obama signed into law a spending bill that includes a provision lifting the ban on crude oil exports. As previously noted, the oil companies have been hard at work to remove the 1970s-era ban.
Many feel that lifting the ban will stimulate the economy, create jobs, streamline production and stabilize the worldwide price of crude oil (and gasoline). Many others are concerned about the effect on U.S. refineries and jobs in the industry. Some policy makers believe U.S. crude should stay in the U.S. to further decrease dependency on foreign crude.
It is possible with the price of oil so low that not much U.S. crude will be exported anyway. As of this writing, I am not aware of any requirement that the oil be transported on U.S. flag vessels with U.S. crewmembers.