Historic fabric does not necessarily refer to the buildings physical fabric. It also refers to its overall atmosphere. Such things as its viewscape, it's lighting at night, and other intangibles can also be historic fabric. So, if a house is widely considered to be haunted, would eliminating the ghost be harming historic fabric? If I removed a painting of the home's most famous occupant, that would be damaging to historic fabric so if I remove the dead occupants spirit, I would think that, too, could be harmful. If I don't know the importance to the house of some physical material, like, say, some wallpaper, I let the wallpaper remain until it has been thoroughly researched. If I don't believe in ghosts, I should still remain objective in case science proves their existence later, and not exorcise the ghost. Are there any experts from haunted house museums who can offer an opinion?
I do not work in an historic house that's supposed to be haunted, but I've read a fair few emails on the Museum-L mailing list on the subject. For the most part, the attitude is that all paranormal investigations outside of a sanctioned "ghost tour" are potentially dangerous to the house itself and its furnishings, since people can bump into things, film crew setups can knock something over, etc. The idea that you should keep an open mind in case science later proves that ghosts exist and make sure not to remove one is very fringe among house museum professionals, if it exists at all there.
If someone did believe that an historic house was truly haunted, they would probably consider that the ghost belonged to the house and not exorcise it. But anybody waiting on proof that ghosts exist would very, very likely not sanction an exorcism at all.