The strength of those instincts does vary from cat to cat though.
I have two cats, and one is a cold blooded killer that'll attack anything that moves, including my toes. The other will just sniff spiders and cuddles rabbits and hamsters. It did once chase a small mouse, but once it had it cornered, it didn't do anything.
Cats and rabbits get along well because cats think grooming someone is dominant, but rabbits think being groomed is dominant, so they both think they're on top.
Domestic rabbits are the most attitude-y animals I've kept, with such surprisingly variable personalities.
I had a rabbit that we'd let out in the garden, and if the neighbour's cat came in the garden, the rabbit would chase it out, and even attack it if it wouldn't leave.
I have two cats, and one is a cold blooded killer that'll attack anything that moves, including my toes. The other will just sniff spiders and cuddles rabbits and hamsters. It did once chase a small mouse, but once it had it cornered, it didn't do anything.