My cat ignores mirrors. He also ignores screens and isn't bothered by audio of dogs or cats. At the same time, he's very alert and will generally spring to attention if he hears a dog or cat outside. A few years ago he was introduced to another cat, separated by glass, and his reaction was completely different compared to looking at a mirror. I don't remember the first time he saw a mirror.
I think that cats have a pretty decent idea of what is and isn't real. While a reflection may be interesting in that it looks like another cat, it lacks the accompanying sound and smell of an intruder and is therefore safe to ignore.
On a related note, many years ago my family lived in a house with a lot of bird life in the back yard. There was a family of magpies, a number of chickens and a solitary male guineafowl. While moving in we leaned an old mirror against a fence in the yard and it ended up staying there for years.
Initially, the magpies attempted to fight their reflections but they quickly learned that there was no point. After that they ignored the mirror. The chickens never seemed to notice it in the first place. The guineafowl, though, was most interesting. This is a species that forms flocks in the wild. This particular guineafowl, though, had been separated from its flock for years and was completely alone. To begin with it had the same reaction as the magpies and attempted to fight itself in the mirror. Over time, however, this behavior stopped. Instead of fighting, it would simply stand in front of the mirror for hours on end.