Oppenheimer, a determined Leftist and almost certainly a communist and source for Soviet spies... As they had Oppenheimer under strictest surveillance and surely were reading all his mail and screening his calls BEFORE the project I can't see where you're getting your information.
That WAS an era where too many were blacklisted being in the wrong place at the wrong time when too many in high government positions actually spying for the Soviets lived, got traitor money and died never being found out.
For an introduction to the subject, consider:
Was Oppenheimer a Soviet Spy? A Roundtable Discussion Notably, the best evidence -- that of the Soviet era spy archives -- remains closed, but the trend of disclosures increasingly favors the view that Oppenheimer was a Soviet spy or a knowing source for them in one sense or another even if not formally enrolled as a spy.