Would FBI agents really care about civil rights?

Because unlike the CIA the FBI cares about it's public image. J Edgar Hoover put a lot of effort into making the FBI look good in media and that tradition continues to this day. How many TV shows/movies have you seen with the FBI being "the good guys"? How often does that happen with the CIA? The FBI has a reputation in popular culture and they value it.

---
I'm now 20% cooler

You're right. They dont like civil rights.

They love the *hit out of the Patriot Act. They do like the law though. Nobody in the US would like to be legal liability.

What was portrayed was not the FBI being civil rights arbiters, but Denzel Washington's character being the crusader and believer in "the right way" as the CIA agent said about him and his history.

I liked the movie, but it became a little 'preachy' at the end.
Finally, I don't think that during Marshall Law the FBI is going to have any jurisdiction over the military.
If anything, Anthony Hubbard and some of the other ranking FBI agents would have been locked up to prevent interference with the Army.

Well, to be fair Denzel doesn't just go to the Army barracks and takes Bruce Willis into custody out of a whim. He had a court order. I'm not sure if that would amount to anything - Bruce Willis clearly says that his authority overrules the court - but I guess that a FBI agent who refuses to serve a court order would be in contempt of court or something. I'm not familiar with American law, and even less with American Martial Law, but I guess that court order gives Denzel the authority to arrest the Army's hot shot. This is a Hollywood movie after all, even if it deals with controversial and political issues, I don't think that legal accuracy was on the minds of the filmmakers.

And if some (or even most) FBI agents don't care much for civil liberties, Denzel does in the movie. He's the classic hero who does things by the book, and who believes in the Constitution even in difficult times. If he went out torturing the hell out of suspects, then he pretty much would've been the same as Bruce Willis, thus invalidating the point of the movie - to put it in a very inarticulate way, the point being that government suppressing civil liberties is a bad thing.

the FBI is a government entity, and like any government entity, it has the responsibility to represent and defend the laws for which they stand for and operate under. That includes the constitution, which includes the First Amendment. You don't have to be a civil rights attorney, or a ACLU member, or a community activist to care for civil liberties.

I believe you mean civil liberties. Civil rights refer to equality like anti-discrimination laws. Civil liberties are basically human rights that are protected in the US Constitution (liberty to defend yourself with firearms against criminals and tyrants, freedom of speech, the right to defend yourself in a court of law, etc).

As for your question, Denzel's character is an FBI agent and all law enforcement officers are required to take an oath to protect and defend the US Constitution (not just politicians) Furthermore, Hubs seemed to understand basic human rights (remember his speech about how the terrorists already won because they declared martial law?). It really all depends on how educated FBI agents are about civil liberties and if they even care.