Most fursonas do wear clothes. But putting aside the aesthetics factor and focusing more on the practicality-- would a furry anthro in an anthro society wear clothes?
Focusing solely on mammalian anthros with fur. Well, they have fur, so temperature regulation and the elements aren't really reasons to wear clothes given that they have natural, furry clothes already. Wearing clothes on top of that might be too warm, especially in the summer.
The thing I'm wondering is, would anthros figure out to make clothings themselves? And if they do, how would they look? Having their body completely covered in fur might make shirts and pants irrelevant, which means they might never develop them in the first place. I suppose other articles of clothings like armbands, headbands, etc would still exist, and so would practical items like glasses or watches.
Of course, clothing serves more purpose than just covering bare skins. They serve aesthetic purposes and shows our identity. For example, police anthros might wear some sort of stuff to distinguish themselves. And much like humans, anthros would probably have a culture around clothing, but how their clothing would look and how much it'll cover is the question.
Would most anthros only wear head and armbands? Maybe just something to cover their bottoms and nothing else? Or would they wear clothes similar to us?
Furthermore, different animals have different fur with different thickness, length, shapes, forms, etc. These different furs require different clothing. Anthros with thicker fur may wear less clothing than ones with thinner fur. Even more, different anthros will have different body shape and size. Clothing for rabbit sonas may not fit bear sonas.
Anthros might have different size standards for different species to account their differences. Imagine how hard it'd be to manufacture all the different variations, though. Any clothes store would have to take into account multiple species and multiple sizes for that species.
Well, I think that's interesting to think about.
While this is heavily species dependent, assuming a highly diverse set of species, I'd imagine at least a part of the cultural evolution would be clothes as a tool for courtship, not necessarily protection. Covering up the naughty bits, showing off status through fashion, hell even basic clothing for specific jobs (however minimal they may be) are likely occurrences in such a setting.
And to piggy back off the multi species tangent; I'd imagine the less fur you have (or fat) the more likely you would be to wear clothes for comfort or protection. The size problem is simply resolved less through diversifying the clothes, but modularization. Foxes don't wear pants, they wear togas. Lizards wear leather straps around their girdles, birds might only ever had a bandolier and a hat. You don't buy a shirt, you buy a strip of cloth with sleeves. Then you tie it around you and secure it with a clip.
The diversity surrounding species variety would motivate eclectic industries capable of handling multiple different forms and needs. A niche, unless highly ludicrous, would be doomed financially.
EDIT: Negating courtship is also a reason for clothes such as in a business