Yeah, despite the hip, urbane and ever-so-cool kind of feds you see on Criminal Minds, the FBI is (as it always has been) one of the most up-tight group of predominantly straight, married1 Catholic men you're ever going to come across outside of a church. It has a long-standing corporate culture that has seemed (for better and worse) to be pretty impervious to change.
Other Federal Agencies with police powers have different cultures, from the DEA which likes to hire cowboys (tons of ex-spec forces types), to the Treasury Department which seems to have a pretty diverse culture inside it.
All of them though really want only top students from top schools.
1. They really want you to be a lawyer or CPA too (though engineering and chemistry have also been popular of late) They tend to look down on criminal justice majors, for the FBI a Criminal Justice degree is pretty worthless. Like most federal jobs, few people without the proper education get in. The FBI and most federal 'special agents' require a degree from an accredited 4 year college - and a terminal degree is even better. So a JD for law, a PhD for chemistry, and the schools are mostly the Service Academies and Ivy League, like most high ranking federal jobs, though NYU, American, Fordham, GW, Gtown, University of Miami, Northwestern, Georgia Tech, Emory, Boston University and Boston College are also popular) Though to restate what I said to begin with: They really want you to be a lawyer. The high number of lawyers who are special agents is part of the reason for the FBI's conviction rate.