r56 Oppenheimer had two partners, immediate family & friends/colleagues who were members of the Communist Party in the 1930s. One colleague actually approached him about spying for the then Soviet Union. He turned him down, but didn't report the man to the government.
NTS, this caused problems with the military and civilian brass who oversaw the Manhattan Project. (They had Oppenheimer under surveillance anyway because of his leftist opinions alone, and also because the closet case FBI prick bugged anyone left of centre for his own political capital.)
The Project's military commander, General Groves, had an uncanny ability to understand the eccentric personalities of elite scientists (especially for a conservative military man). He knew many academics were leftists, had a 'fuck you' anti-authority streak, and were politically clueless, generally and in the 'office politics' way. He sized up Oppenheimer as a genius prick with a sharp tongue, but nevertheless a loyal American. He decided his value outweighed any Communist associations, and he knew the FBI's blanket surveillance would catch anyone dangerous around him.
Others disagreed, and thought it was not unreasonable to consider him a potential national security threat. Some even thought he might have actually passed information to his friend as some point, but didn't have concrete theories or confirmation from other sources.
He famously lost his government security clearance after the war--although by then, it was a political, careerist move by his enemies as well as a genuine national security concern. The most reasonable opposition to him re: his past was that he was very against some aspects of nuclear weaponry, and it was felt that he might leak info to the Soviets out of a philosophical idealism, similar to Klaus Fuchs.
Of course, antisemitism also reared its ugly head--the trope was that Jews were not 'real' Americans and at the end of the day, they can't be trusted.
When the KGB archives were opened decades later, Groves' assessment was proved correct--something that could not be said for other Leftist martyrs, like the Rosenbergs.