I think you should go with your instinct and look for another dog.

Even if the dog tolerates the ca, it has a high prey drive. This means if a cat dashes about (and what cat doesn't at some point?) the prey drive will kick in and the dog will be on the trail.

My dogs don't catch birds. My dogs get along great with my cats. Yet the one time one cat scooted out the door into the back yard (and hence was running freely with abandon loving the game of "mom, catch me if you can) the dogs set out after her. (They were already outside.) She had the sense to dash into the garage and up on the car. Back in the house, I noticed that when the cats rush around, the dogs do trail behind barking. Why I hadn't noticed it before I can't say.

You will need to be alert constantly if you have that particular dog in the home. Constant alert is difficult to maintain.