A recent study tentatively concluded that purebred cats are friendlier than mixed-breed cats. It's a pity that study was so inept, though. It has been fairly well established decades ago that the single biggest predictor of a cat's friendliness toward humans is how much it was handled during its earliest weeks. Without controlling for this factor, any study on cat personality is going to be totally off base.
Cat racism kills - black cats don't get adopted.
Purebred cats will generally get a lot of handling from birth to the time when they leave for their new families. Cat breeders for the most part are in it because they love cats, and any reputable breeder will be spending a lot of time handling and cuddling their new kittens.
The same is true of many mixed-breed litters. A lot of cat owners are delighted at the prospect of kittens, and will be handling the kittens a lot during their earliest weeks.
But then you have unscrupulous cat breeders who leave their cats in cages from birth to death. Kitten mills, like the ones which ship kittens to pet stores. These kittens are poorly socialized at best; nearly feral at worst. And the same is true of many mixed-breed litters born to cats of uncaring owners.
Another (far better) study examined people's perceptions of cat colors and personality. People were shown pictures of cats and asked to describe them. This study showed that people believe orange cats to be the friendliest (as the [extremely biased] owner of orange cats, frankly I agree). White cats were considered aloof, black cats antisocial, and tortoiseshell cats were thought to be "intolerant."
Over the years, I have had many otherwise sensible people tell me that they firmly believe that coat color influences cat personality. One person told me that black and white cats are "always crazy."
I'm open-minded about the idea that coat color and personality could be connected. But if there is a connection, it's obviously a weak one. A broad statistical study would be relatively simple to do (just poll cat owners about their cat's color and main personality trait). I would be very interested to see the results.
But on the whole, this kind of thinking amounts to cat racism. And it is literally a life-or-death matter for cats in shelters. White, black, and tortoiseshell cats are adopted at a far lower rate than orange cats. When a cat doesn't get adopted just because of prejudices regarding its coat color, more often than not, that cat eventually has to be euthanized.
The next time you're thinking about adopting a cat, keep an open mind about the color!