It's not an exemption from investigation, just not having FBI agents try and interview him without a go-ahead from the higher ups. Since they can't force him to respond to an interview request anyways, and he's said he won't do them, it's seems like basically just a time-saver.
From the file and the Nuclear Security blog post above, it looks like Feynman was considered for a position on a gov't science advisory panel in 1958, the background investigation became concerned because of his safe-cracking hobby, his one-time friendship with (Soviet spy) Klaus Fuchs and a poor character reference from an angry ex-wife. After several interviews, Feynman said he wasn't interested in being interviewed any further.
As he never served on the panel, he presumably withdrew himself from consideration or the gov't decided he was a security risk. As a result, there presumably wasn't any reason to investigate him further in any case.
From the file and the Nuclear Security blog post above, it looks like Feynman was considered for a position on a gov't science advisory panel in 1958, the background investigation became concerned because of his safe-cracking hobby, his one-time friendship with (Soviet spy) Klaus Fuchs and a poor character reference from an angry ex-wife. After several interviews, Feynman said he wasn't interested in being interviewed any further.
As he never served on the panel, he presumably withdrew himself from consideration or the gov't decided he was a security risk. As a result, there presumably wasn't any reason to investigate him further in any case.