Dogs and cats tend to not get along, which is normal in some situations. What is NOT okay is that your dog is growling at ANYTHING while at his food bowl. Food agression in ANY form directed at ANY target is NOT okay.
The fact that your trainer told you that "a dog that doesn't growl is a dog that bites without warning" would be enough for me to find a different trainer. My dog doesn't growl at much of anything, and has never ONCE bitten anything without warning. Come to think of it, he's only bitten one thing. That was a dog we eventually rehomed. She growled at him over HIS food dish (I fed them seperately). He grabbed the back of his neck and tossed her across the kitchen. Mind you, this dog was a bit shorter then him, but about the same weight, it was not a puppy nor a smaller dog. And, yes, BOTH dogs were corrected for doing this.
Food agression is a starter agression, and can lead to other forms of agression. If you allow your dog to growl at ANYTHING over food, he may eventually get the idea that food agression is okay, and may end up turning his food agression towards you. You should correct him ANY time he growls over his food. We corrected our dog for this by giving him a firm no and removing his food until he calmed down. May sound cruel, but it worked. (I get yelled at, etc... for this method all the time. I'm not saying it works for EVERY dog, but it's what has worked with mine. Those that don't like the method are perfectly entitled to their opinions, and I do respect their opinion on this method.) To this day, cats, other dogs, and even my two year old son, can get near my dog (yes, I supervise my child when he's around the dog) while he's eating with no growling, etc...
In most cases, dogs growl over their food as they see it as THEIRS, and they feel they need to protect it. If it goes uncorrected, this will eventually travel to toys, treats, etc... And the dog may end up actually hurting the cat if it's not corrected. Also, even if the dog doesn't growl at you, in the future, he could snap at the cat and accidentally get you in the process, given the right situation. I know it's possible, as I've seen it happen. I've seen a person end up in the hospital because they let it go as "normal". One day, their dog did more then growl, he went at the cat, and got the person's leg in the process, leaving a pretty decent bite wound that needed medical attention. The dog had NO intention of going after the person, but did so by accident. I'm not saying by any means that this WILL happen to you, just saying that it COULD happen and HAS happened to other people because they let their dogs growl at cats, etc... around their food bowl and said it was "normal" and brushed it off, leaving it uncorrected.
Dogs that don't growl at NOT unpredictable, they are well trained. Dogs don't always growl before they bite, they show other signs such as arching slightly or stiffening their backs, baring teeth, etc... Biting does NOT always follow biting. Honestly, I'd see if you could find a different trainer. Just my opinion, however, you can do with it what you will. I will tell you that (from experience in having dealt with other people's dogs), food agression does NOT fix itself, and it is NOT acceptable, and NEEDS correction, even if it IS just at a cat. Like I said before, it's a starter agression, kind of like a window for other agressions to form. Best of luck, and I hope this was at least somewhat helpful.
Current dog owner, and have also worked with dogs belonging to family members, friends and friends of friends. I like to think I know a thing or two, lol