I guess it depends on what sort of life said fur leads, and what type of world he or she lives in. If he/she lives in a forest, with not much contact with others, I don't see why he/she would need clothes.
I guess if the world is like ours, they'd probably wear clothes, because we do.
On the other hand, my fursona, Junyad Van Bloodmourne, was brought from earth (as a human) to a different world, and most furs there DO wear clothes.