I've had my own dogs seriously injure a cat of mine. That cat and that same dog lived in harmony for nine years after the incident - I'll never know what set Ben off, but he was a pup at the time (about the same age as your foster, in fact). I know from working with stockdogs that prey drive often peaks between six and fourteen months. Prey drive is the "I wanna" that allows dogs to take training even when the going gets tough. Then they grow a brain which regulates prey drive - what I call impulse control. But impulse control has to be encouraged.
Contrary to popular thinking, bully breeds have superior natural impulse control. Part of what freaks people out about the way they come on in an attack, is their cool-headedness. This dog is not purebred, so you can't count on that, but it is not the bully breed in your foster that might make him unreliable. When I think "reactive" I think more of herding breeds, really.
Okay, enough theory, on to the practical. It's incredibly silly to think of putting down a pup for killing a cat. I lost a very sweet cat to a foster last year, so I've definitely been there and know how it hurts. But I know the risk since I take dogs who have prey drive right at the top of the scale (would your dog run 1000 yards on the off chance that there might be one bird which they can't see and which they know will fly off the second your dog comes into sight? If so, consider a career change for your dog - airport bird strike patrol).
The reality of life here is that the dogs must be under tight control at all times - because the cat is free to move around and might be anywhere, anytime. The dogs have very solid recalls, but I'm not perfect - and Border Collies are very fast (that's how Curly got my Siamese last summer).
The thing is to put something in your pup that will make him hesitate for at least a second. Two things. One, every time your foster looks at a cat, say, "NO!" After killing a cat, I assure you that when he's looking at a cat, there's only one thing on his mind, and you can associate that thought with the idea that it makes you unhappy. Second, follow the correction quickly with a command - use the same one each time, recall, sit, down, pick up a rock - it doesn't matter. Then reward him for looking at you and following the command - but never reward him for looking at the cat.
Do this often enough, and he'll have another behavior conflicting with the initial impulse to chase. This is not a fix - you will never make him "cat safe." What it will do is ensure that you have a second to prevent any accidents - that second where he's considering whether to follow his instinct or his training. Continue with it and his training will win pretty much every time. This is how we train one of the most prey-driven breeds in the world to walk calmly amongst sheep without requiring a leash, ever.
As to adopting him - I don't find adopting out dogs that are cat-killers, a problem. People understand that some dogs don't like cats - heck, it's an image most grade school kids understand from cartoons! You don't let such dogs roam the neighborhoods off leash (duh, I wouldn't adopt to someone who planned to let their dog roam anyway), such dogs can't go visiting in homes where there are cats and probably small dogs I'd guess in the case of this dog, and probably PetSmart or an unsegregated dog park isn't the best place to socialize such a dog.
There's a huge difference between dogs who are simply following prey drive, as in the case of this pup, dogs who are dog aggressive, and dogs that are aggressive towards humans. The last two are social problems requiring specialized training, the first one is natural and can be managed very safely.
Remember (and remind your group) that aggressive actions are discrete behaviors and clues as to underlying personality traits. They should not lead to labels, which are quite unhelpful when trying to address unwanted behaviors. Treat the things a dog does as the dog himself understands them, one behavior at a time, and the dog himself will give you the answers you need. In this case, your pup is merely showing you one side of his developing personality - a high prey drive - which has the potential to be redirected to more constructive things like fetch games, tug games, and sports like flyball.
I have yet to find any behavior in a dog which didn't have the potential for what we would consider good when redirected. Sometimes I fail at redirection, but that's my limitation, not the dog's.
That helps me when "bad" things happen. A couple of weeks ago I got bitten, only the second time I've ever had a dog land a bite in seven years of working with problem dogs. I knew this dog had the potential, but could never get her to show me that side in her. I knew she would do it because of other signs I'd seen - she doesn't like being handled and her collar especially was a point of tensiion.
But I wasn't ready when she finally went there. The reason I wanted her to make that choice, though, was that she had been abused and was very shut down in a weird Border Collie way. I wanted her to know that anything was fair game, before she went anywhere else.
So whatever it was that day, I reached down to take her collar and "encourage" her to do whatever and she turned and nailed me - twice! Yikes!
As usual I went into my "wrong choice" mode, and then took her collar again. This time there was a huge difference in her attitude about my touching her collar, and the second she gave me that, I took my hand off and simply let her through. Bet simply had to know that if she made a wrong choice, I would be fair in the way I communicated that. She made a boo-boo, and found out she couldn't get away with it, and she was neither hurt nor neglected for it (she has experienced both on multiple occasions).
Since then her big giant problems with pressure, with freaking out about being "messed" with, and other things like her nervous OCD pacing, have all turned into something else. These things don't go away - if one lets them, they become what they were meant to be in the dog.
In Bet, she is a very "busy" dog, highly concerned about everything, which led to her making odd rules about being touched and being interfered with while working. But now she knows she doesn't have to have all the answers (and more importantly, she won't be harmed or hurt if she comes up with a wrong answer), she comes up with very nice answers within the scope of what a dog can deal with. She is always at the ready to spring into action, and knows just what needs to be done, where I have to do a bit more 'splaining with Gus and Ted. Where before she burned tons of calories pacing literally all day, now she resides on the couch where she can be ready if anything happens, and I've had to reduce her food about a third though she's now doing twice as much work as before.
So, my point is that you have to channel your feelings about the violence, to understanding the part of the dog that it comes from, and seeing whether you can tap into that to possibly even increase the adoptability of your foster dog.