Count me in as another “give it a try under close supervision”. I have no experience with rabbits, but I have shared a home with two cats that got along quite well with my pet birds.
O’Brien the Budgie was actually brought home to be a companion to my ex-cat Conan after we had to give up his pal Schrodinger. Unfortunately, we ended up giving Conan up as well, but for a couple of weeks, it was hilarious watching the two try to play together. Conan would pounce on the floor inches from O’Brien, then sort of sit there and wonder what to do next. He would lie down, O’Brien would try to preen his whiskers, Conan would jump away. Sometimes if O’Brien was sitting on a basket or rung of a chair, Conan would try to pet her with his paw. It was soooo cute… Conan, btw, had been raised from kittenhood around a cockatiel, which escaped one fine day while I was at work when the Mango Tree left the balcony door open so the cat could go in and out, then didn’t supervise the bird. Since then, I’ve been quite the harridan when it comes to the pets. Mom’s actually starting to listen, even.
But, to get back to the OP, cats can get on quite well with prey species if they’ve been raised around them. Even if they haven’t, a cat that hasn’t learned to hunt (kittens have to be taught this by their mamas) and has been an indoor kitty all its life may not regard the “prey” animal as food. At worst, there may be a bit of chasing and pouncing, claws retracted, followed by a look that says, “tag, you’re it. Um, you’re supposed to chase me now. Oh, you’re no fun anymore, I’m going to go play with mom’s knitting wool.”
A cat that’s an outdoor kitty may be more of a problem. It may have been chasing birds and other small animals and figured out how to kill them, and that spells trouble for bunny.