One of the races in my world is a fox-people. They are basically small humanoids with a few vulpine features, including ears and a tail. They live primarily in a sub-arctic climate, where their additional fur is a benefit. Technology is very roughly 16th century European. I had imagined there were individuals of other races (let's just say humans for simplicity) who would also be living in the same region. Initially I had pictured these individuals as the equivalent of mountain men, living off the land and dressing in furs they had trapped. This, however, presented the question of how their dress was perceived. On one hand I can see how this would utterly horrify a people who also had fur. However, then I thought about how (most) humans are not bothered by leather goods, despite also having skin. So the question is, would the fox-people be offended by fur clothing?
"What, can't you tell the difference between fox hair and human hair?"
There are many types of fur, with varying qualities, such as thickness and length. Further, fur is indistinguishable from human hair on the structural level - that said the expression of hair and fur varies greatly between animals.
Humans consider their hair different from that of other animals, just as we consider human skin different from that of, say, dolphin skin (even though both are mammals). We make these distinctions readily, and there is no reason an intelligent race of foxes would not. Thus, it is unlikely that wearing a bear pelt would be any more offensive to them than wearing a human pelt.
Wearing a fox pelt probably would be offensive, just as wearing a human pelt (or human scalps) is offensive to humans, in general. That said, some of the race probably wouldn't take offense, just as some humans seek out such trophies.
Likewise, some members of the species are going to take offense at the bear pelt - but probably in fewer number and attached to a concern that is different from raw existential disgust. In this way they'd be similar to human PETA activists.
In short there is going to be a spread of opinions, and a spread of ability to distinguish particulars about a given pelt or skin. It is unlikely to rise to a level of a species-wide more unless there is another instigating factor. As a comparison, take widely varying opinions on what is taboo food to eat in human cultures: each of cow, scorpion, beetle, dog, monkey and human is acceptable to eat in some places and not in others. The widespreadness of those taboos is in part proportional to their closeness to human-ness, and in part their closeness to other-ness, but all are accepted in places and rejected elsewhere.
This seems more like a society thing than a species one. As you said yourself, humans have skin and most aren't offended by leather, which is derived from the skin of animals.
I'm sure your world may contain fox-persons who are offended by fur products, but I'd rather think fur products would make a great societal/fashion statement. Foxes are omnivores, like humans. Presuming the fox-people follow the common diet of the fox, they eat meat. A number of humans prefer to hunt their own meat; no reason fox-persons wouldn't also. Since it's unusual to eat fur (seriously, I can't find a single article online stating whether it's safe to eat fur), the fox-people could just as well take the fur and use it as a symbol of their hunting prowess: "See this cougar fur? Yeah, I killed the cat myself."
If your world has both fox-people and foxes, killing a fox may be a taboo in some cultures, just as some human cultures have a taboo about killing apes or monkeys.
There was some flavor text on a Magic card that I will sum up. Essentially it would be worth your life to wear lizard skins in the desert because the reptilian people living there were mightily offended by it.
I found that to be incredibly absurd, and compared it (as you did) to mammalian races wearing leather.
That being said, how similar would an item made of fox fur appear compared to the same item were it to be made from the skin of your fox-people?
If the similarity requires a second look or deliberate study to tell the difference, this may be quite offensive. This may increase to a fatal mistake if there is history of fox-people actually being "harvested" for their fur.
The actual quote on the "Viashino Warrior" card is:
When traveling the Great Desert avoid wearing the scales of lizards, for the Viashino rule the sands and look poorly on the skinning of their cousins. --Zhalfirin Guide to the Desert
Probably not. We wear leather, and we have skin.
Your fox people know the value of fur in a cold climate and probably have beauty standards related to their fur, so I think they would understand other species/races wearing furs of the same reasons. They also won't necessarily see themselves as animals or animal-like, even though we or other species/races in their world would think there's an obvious connection.
They would certainly have a problem with their fur being worn by others, just as we cringe at the idea of people being exploited as a resource.
As other answers flesh out human based and non-human based leather are very different things only to humans.
If they are not vegans they probably aren't going to get that upset by seeing dead animals. Then again if they are content to always dress in their birthday suits it might strike them as icky to have something dead hanging about all the time.
They might think Humans trying to look like them is flattering, or maybe a little silly. In the 16th century the locals of various non-Europe places (who were often comfortable mostly in their own skin) thought the European's choice of clothing non-obvious.
Everywhere I'm aware of has a tradition of mocking their neighbor's costume that seems to be irrespective of what the costume is or how close it is to their own, but generally the offense of it doesn't last more than a generation of contact.
Why would they be offended? If they're fox-people, that means they're intelligent carnivores. They will not be vegetarian, and will most certainly eat furry mammals with much delight.
If you want them to become offended, weirded out, or sickened by people wearing food, then that might work.
But even if it was foxfur from feral foxes, to them it'd only be about the same weirdness as seeing someone wearing a monkeyskin is to us.
They're very unlikely to relate to their unintelligent brethren unless there's some religious aspect making killing them a no-no.
On the other hand, cultural history could have men killing and skinning them, so humans wearing fur could be seen as a huge slap in the face.
Most societies are for the most part reasonably tolerant of such cultural differences, though, and will just point it out and laugh at the ignorant outsider. To me, an over the top, pitchforks-and-torches reaction, would feel a bit like you were straining believability for the sake of plot.
In the real world, there are humans who are offended by leather and fur clothing, and humans who aren't.
There are even businesses which make articles of clothing out of human leather, even though this comes from willing participants upon their deaths it's obviously a lot more more controversial though is accepted by some.
Similarly, the thought of wearing shoes made from bonobo or orangutan leather would likely provoke more hostile reactions than those made from cow or pig leather.
But it really boils down to their culture. If they're a sub-arctic species they won't necessarily have a lot of luxury and may be fine with it. That said, their views on some kinds of fur may be similar to modern IRL humans views of primate leather.
At a guess I would balance it somewhere between modern human views on primate leather and pragmatic acceptance. Perhaps it's looked down on, but not outlawed because dammit subarctic climates are cold.
You could definitely go either way with this one. On the one hand, humans eat chimpanzees, and seem to have no problem with that. On the other hand, if aliens came to earth and started eating chimpanzees, we might react a little more negatively, given their status as outsiders.
You could also:
Make the animals sacred
Hindus are offended by eating cows, even though they don't consider cows to be their "cousins." Maybe your fox-people believe that fur is a spiritual thing, that the soul resides in the fur or something, but it's not even strictly necessary for this scenario.