In opposing the genocidal policy of confinement and sterilization for all cats, the Cat Sanctuary is not suggesting that all cats can or should live completely natural lives as unaltered barn cats. Many cats, including some fancy breeds, are not well suited for an outdoor life and should be kept as indoor pets if they are going to enjoy the 10-to-25-year lifespan that is natural for the species.
I personally would recommend confining, and sterilizing, long-haired and flat-faced Persian-type cats. If unwilling to keep one of these animals indoors, I'd give it regular haircuts. These cats were bred to require a lot of grooming by humans (and in warm weather they don't seem to enjoy being held and groomed). Outdoors, they attract fleas and ticks. Indoors or outdoors, they shed, lick off, and swallow enough fur to make themselves sick...but they don't reach deep enough into their coats to keep their skins clean. If deprived of the human attention it needs, a really plushy-looking cat will certainly be uncomfortable and will probably become ill.
I'd recommend confining Rex cats, who are genetically doomed to grow incomplete coats that don't provide the insulation from weather conditions normal cats enjoy.
I'd be very cautious about allowing Scottish Fold cats, whose mutant ear shape is said to suggest a hostile expression to other cats, to socialize on their own. Animals have the ability to learn, as humans do, that what may seem like an angry expression is just the way some unfortunate individual looks...but it may take a while.
I personally would also recommend sterilizing Manx and Japanese Bobtail cats. An AC article I wrote on this topic generated lots of opposition, and what emerged from the controversy was that the genetic mutations that produce these breeds are farther-reaching and harder to predict than anyone seemed to have realized. I personally feel that these are dysfunctional genes that should be bred out of the pool.
Then there are problems that appear in the more functional breeds...more about those later.