My brother has a German Shepherd with an incredibly high prey drive - would turn into an unrecognizable rage beast when presented with a cat, it was actually kind of terrifying - and they were able to work intensively with him over a period of months with an e-collar and a very good trainer. He will now call off family cats and is occasionally allowed exposure to them. Never ever unsupervised, and only in small doses. When he visits us, we lock our cat away - too tempting. But I swear I would never, ever have thought they’d get even that far, so I guess there is always a possibility!
Our own mutt (boxer/lab/hound/?) loooooooves the chase but learned pretty quickly with the help of a spray bottle and a good “leave it!” command that there are times when the cat just does not want to play. Cat was never really scared, but lacks the front claws to teach an effective lesson, and the pup has enough Boxer in her to think that pawing is excellent play, so we always keep an eye when they take off running - but she has learned when we want her to quit.
So both dogs will chase cats - but there is a huge gaping chasm of difference between them in terms of trainability, natural instincts, and the intent of the chase. It’d be hard to really figure that out in a rescue dog without some extensive exposure and knowing what you are comfortable training in.
