[komon]

Well, due process is a right co-equal to free speech, so which rights override which others in which circumstances will come down to legal precedent.

My understanding is that the FBI or other non-judicial body cannot unilaterally issue a gag order. Subpoenas and gag orders related to them are granted by judges.

(Which isn't to say that the relationship between the judicial branch and law enforcement bodies is always pure and equal)