FBI is rabidly conservative. This isn't a secret.
Seems to me it depends what you are comparing it with. On the one hand, weirdo J.Edgar's paranoid form of anti-communism seems as if it embedded conservatism into its culture (e.g his determination to 'get' MLK), but on the other hand, it has also warned about the infiltration of local police departments by the far-right, and has occasionally been less racist than those local PDs (which isn't saying much, though, as some of the latter have resembled branches of the KKK).
Similarly, the CIA, while firmly anti-communist, seems to be more socially liberal (and maybe a bit more reality-based than the Pentagon, from what I remember reading of its more pessimistic reports about the Vietnam war). Both of which traits came out in its sponsoring of abstract expressionism - a policy intended as anti-communist but which seemed to end up upsetting the socially-conservative right.
It's just vaguely interesting how different parts of the state apparatus tend to have slightly-different cultures (e.g. NAOAA at one time being more sympathetic to climate-change denial than NASA)