On a theoretical level, I understand the predator instinct and the inherent risk. On a personal level, we have not had any issues with *our own* cats. When we first got chickens, we had 2 middle-aged cats who had started as indoor cats for the first few years of life and became outdoor/indoor cats. The girl cat, Puss, never showed any interest in the chickens, even when they were chicks. The boy cat, Linux, was very interested in the chicks but had no way of getting to them even if his intents were "instinctive." When the pullets got to about 1/3 their adult size, he pretty much lost interest, and the first visits in the yard were always supervised. As they grew, he actually started hanging out in the yard with them and chasing off neighborhood cats who tried to come in. Puss continued to show no interest and preferred to hang out in the yard that doesn't have chickens. Spring of last year, Puss and Linux passed away within a month or so of each other, and we saw an immediate increase in the amount of neighborhood cats sniffing around the yard. A few months later (during the gap when we had no cats) we had our first (and thus far only) predator loss, the smallest of our flock, a bantam cochin pullet. We assumed it was a neighborhood cat because my daughter mentioned she had seen one on the fence shortly before. Due to that, and the face that we seemed to also be developing a rodent problem since the cats' demise, my husband immediately decided we needed more "guard" cats and we went out and adopted 2 kittens the next day. They started indoors and eventually we started letting them out for supervised visits in the yard and now, their actions are the same. Girl cat Flower prefers not to go in the chicken yard at all, boy cat Curious Corn (C.C.) started off being scared of the chickens (and they do chase him if he gets too close, giant hens and bantam roos alike) and now they hang out together in the yard, and he keeps the neighborhood cats at bay.
We also had a dog for a while, and he never hurt the chickens, but his jaunts in the chicken yard always had to be supervised/on leash because he did enjoy chasing them and tried to play with them (though he had many opportunities to kill he just acted confused when he reached them, and we didn't want to stress them or risk having him "snap" one day or hurt them accidentally).
At night, we roll the dice I guess, because our risk for nighttime predators seems to be low. I think C.C. (and possibly Flower, i don't know what she does at night) patrols the yard but it's hard to say how regularly.