In the fortean community, the Scully type is typically called the 'pseudoskeptic'. This is a reactionary type, living to 'debunk' anything that runs counter to his or her existing model of reality. The 'debunking', upon close inspection, loses its thin pretense of rationality and is exposed as a simple mammalian response to threat. In the case of the pseudoskeptic, the threat is typically conflict with whatever they learned in high school science class, and it highly resembles the response of a religious fanatic when dogma is directly conflicted.
In the skeptic community, the Mulder type is typically called a 'woo'. This type is also a reactionary type, living to 'prove' the existence of something that runs counter to the consensus model of reality. This 'proof', upon close inspection, loses its thin pretense of truth-seeking and is exposed as an application of wishful thinking on a large scale: the 'woo' wants to believe, and will ignore any evidence to the contrary.
These two types are actually not terribly dissimilar. They are both true believers, living to validate their own personal views of the universe. The main difference is that the pseudoskeptic has a model of the universe very close to that of the consensus, while the woo has a model of the universe that is very different. It doesn't matter whether or not the models are correct or have predictive value; truth ceases to matter once belief takes the stage. Despite the cries of the pseudoskeptic, neither of these types are skeptical, either. The skeptic actively questions both assumptions and claims, while the pseudoskeptic merely 'debunks' them.
Fortean anomalism is on the fringe of known science, and can be expected to stay there indefinitely; anomalists seek the fringe of the known, and inhabit the borderland between the mundane and the batshit darkness just beyond it. This doesn't make skepticism less important: it makes skepticism more important, and makes belief even more dangerous. There is a tendency for the mind to see what it expects; the mental model affects perception as much as perception affects the mental model. Since the anomalist deals with the unknown, the tendency to see the expected (be it a weather balloon or a piladean missile defense system) has the ability to completely incapacitate the anomalist's ability to see what's really there. Carl Sagan once said that "extraordinary claims require extraordinary evidence", but that is no more an excuse for pseudoskepticism than it is for woo: the anomalist seeks what evidence exists, and if the anomalist is handicapped by a need to see something either more or less extraordinary than that which is there, who will find such evidence?