When I say they have been allowed to growl AT me- we explore the cause and train to remedy. A dog I have owned for years should not STILL be growling at me over, say, removing a toy. We work on those issues.
There are certainly different growls. Current dog is a grumbler... low, grumpy, drawn out growl. That is how he complains about the multitude of injustices in the world. It is not serious "I'm going to eff you up" growling and it does not bother me in the slightest. The "serious" growls are reserved for strange noises and food aggression issues... which yes, we have worked on, for years, and have made much progress, but he still will growl if I push the line to far, and that is OK.
He will also still, very rarely, growl at the cats when they have crossed a line. I also think this is acceptable. The cats are trained (really, you can train cats people!) to respect that growl. He doesn't do it often and the felines understand. I would much rather he tell the cats "Please get out of my face" than just rip them apart. For the most part, the dog is trained that the cats are the lords & masters of the house and he must be polite to them. When they are blatantly being jerks, he may tell them to respect his space, as they have the whole danged house and his space is pretty clearly whatever footage he is currently occupying. They must respect that.