For me the key argument is if you're creating more demand for such things to be created.
If you go to the supermarket and buy meat, clearly you're creating demand for more animals to be bred, raised, slaughtered and delivered to the supermarket.
If you buy a puppy from a puppy farm, you're creating more demand for more breeding dogs and puppies to be kept in awful conditions.
If you adopt a rescue dog from a charity, even if that dog originated in a puppy farm, you don't create additional demand for more puppies to be bred in poor conditions.
If you wear vintage fur, but would never buy something new, you're not creating additional demand for more of it to be created.
Both rabbits and foxes are routinely shot because they are pests that can seriously affect farmers. Rabbits are non-native pests. Personally I'd prefer that the whole body of such animals was used, rather than left to rot - one of the cornerstones of sustainability is to waste nothing. Even as a vegetarian, if I hit and killed a pheasant on the road I'd stop, pick it up, offer it to DF for eating and if he didn't want it then I'd feed it to my dog.