A friend of mine bought up a good point about how awkward it would be for anthropomorphic animals who have more human qualities to their anatomy would be partially clothed. Often going bare in areas that would need the most closure. ;) I can agree with them on that actually!
It's never explained why certain animals are more clothed than others in the comics. In fact, there are some who are more realistic in anatomy that go full bare while others who are more toony are only seen fully clothed. This seems to be a gender issue in some areas depending on the age of the character among other things ect. But that's only a guess on my end...
So! Here's where I try and bring some logic to the way Mobians dress. :D
Most Mobians who reside in places where few humans live wear little to not clothing. The most a Mobian might wear are shoes if their feet are exposed to harsher ground. But as a general rule, many Mobians find clothing to be unnecessary when they have fur or other physical attributes that keep them comfortable in their environment.
Mobians that adhere to this are mostly nomads, or dwell beyond human or Overlander contact.
Despite the presumed superficial reasoning Derps has provided for his eye and wrist wear; other Mobians do make exceptions as to why they wear clothing that's not physically necessary.
Mobians that need to express social hierarchy in complex communities generally go partially clothed like Derps. Mobians that are law enforcers, rulers, generals, ect. often wear only what's required to define them as such from an abroad stance. This can range from top uniforms, hats, or a mix of both.
Mobians who adhere to this generally have had minimal to maximum exposure to humans and Overlanders.
Mobians who go full clothed generally live near or in Human and Over lander societies. While some human / Overlander societies are more tolerant to partially clothed or nude Mobians. Other societies generally penalize and often fine such a visual "offense."
Although this sect of Mobian society constitute as a few; there are some who actually enjoy being fully clothed and even promote it. Some do it for vain reasons; but many enjoy it because it's what they were raised into. Those who cannot wear most clothing such as some birds, hedgehogs, and other animals will either modify their bodies, or their clothing.
Overall, clothing and the use of it when it comes to Mobians depends on the policies, raising, and culture.
And that's my two cents on Mobians and clothes!