I'm in the minority as I don't mind anyone wearing real fur. However, if a company says it is faux fur and they give you real fur, that sounds like bad business to me. I would assume real fur is significantly more expensive than the fake stuff.
I'm the same on the fur issue tbh.
It's become cheaper to use real fur instead of fake (esp when it's "little" things like lining or collars, not talking whole coats), because (as per a docu I saw) it takes ages and costs a lot of money to make the fake stuff appear as good as the real stuff (making the hair look real, soft, get the individual fake hair through the fabric etc). Demand is up for the fake stuff and they just don't have the time and will to work on the fake stuff as much as it takes, so it's become cheaper to just use the real thing. And I suspect that considering the work it takes to make the fake stuff, the fake stuff in the long run can't be cheaper than the real stuff.
Many companies lie, the uncovering of that was quite shocking (same docu as mentioned before). They sell it as "fake fur" to make the sale and appeal to a large crowd, and the amount of what was sold as "fake" but was real was crazy.
Basically, whether Kate's hat featured real or fake fur is hard to clear up, unless someone buys it and checks it (by touching it and inspecting it or making the fire test) or sends it to a lab..
Allergies aren't really to the hair though, but rather to some enzyme or sth from the spit of the animal, which animals of course use to clean themselves (licking themselves clean), which coats the fur and that's what people are really allergic to, not the hair itself (that's what a friend of mine told me, her ex-boyfriend is allergic and she's a huge cat lover, had 3 cats and he could never stay at her place).