Xrhrft

A creature I am imagining is a small mammal about the size of a domestic cat which - through symbiotic bacteria which live in its fur - is covered its whole body over in blue-white bioluminescence, 24-7.

Is there any reason why an animal would be bioluminescent all over its body rather than in just one part or a few parts? The light can't be "turned off". If you need to know; the creature is terrestrial and lives in a forest environment which is, for whatever reason, permanently in relative darkness. It eats fruit, nuts and the like, is social, and not physically dangerous to aggressors (at least when alive, it can be poisonous if necessary).

Note that the method of light production, mentioned above, is also open to change if it needs to do so to fit your answer.

If it is caused by a bacteria, everywhere or nowhere would be the obvious choices for location. The bacteria could even be commensal where it doesn't help or hurt the creature. If the creature has hollow hair follicles for reasons(Doesn't matter really, hold over from arctic evolutionary phase, extra buoyancy, weight, biologically cheaper, etc...) then the bacteria could have evolved to fit inside the hair follicles, (free ride) and the rest is history.

One possible advantage to the creature in this is that the GITD bacteria fill the ecological niche and keep out other things. They live, fill space, photosynthesize and keep other things from growing, much like a good chunk of our gut bacteria serve to slow down C. diff.

There doesn't have to be an advantage though. It could just be something floating around that colonizes the young of the species and short of shaving they never really get rid of.

Bioluminescence in animals generally serves the purpose of sending some sort of message to other animals. These other animals could be members of other species and the messages serve purposes relating to predator and prey interactions or these messages could be intended for individuals of the same species and most often play a role in mating. Bioluminescence has evolved independently dozens of times for different purposes, but here are what I consider the two most likely uses:

Aposematism is the concept of using your conspicuous appearance to advertise that you are unwise to attack. If your animal is poisonous or otherwise dangerous to potential predators bioluminescence might play this role. Perhaps the bioluminescent bacteria themselves are unpalatable.

Sexual selection is responsible for the majority of visually striking animals in nature. In a process known as a Fisherian runaway preferred selection for a certain visual trait by potential mates leads to the evolution of displays that would otherwise be extremely maladaptive. The classic example of this is the tail of the peacock. Perhaps glowing doesn’t serve any real purpose besides making your animals attractive to the other sex.