I don't think rabies would create the zombie like behaviour in humans even with a bunch of mutation. Rabies causes fear and confusion, many animals will bite when they are afraid because that's how they fight, but humans typically not bite as a weapon, we use our hands...

Maybe it would be some kind of fungi mutation that when it infects the nervous system and mess with GABA (gamma aminobutyric acid) and some other stuff... This can change aggressive behaviour in humans, and even though I am not an expert and don't understand the mechanisms beyond superficial level, I wouldn't find it strange if some fungi evolved to make humans feral.

Transmission would probably be through the skin or some other vector of infection that isn't a bite.

As for zombies not attacking each other... It's possible that there would be a pheromone that zombies release that make them less aggressive towards each other... But I'd imagine this would take time before this variabt pops off. If I were to write a book with this premise, humans would artificially produce this pheromone to reduce their risk of being attacked by zombies.

With global temperatures rising, it's reasonable to expect a lot more fungal infections to become the biggest global health concern. Fungi would evolve to survive in human body temperatures faster than we can develop anti-fungal drugs.

I'm thinking less hoards of zombies and more people gradually becoming more aggressive and becoming feral maybe months after initial exposure to the fungi... People becoming terrified of being around other people, and paranoid. Imagine you've had a heated argument with someone and you don't know if it means they are infected, or maybe you are infected. Imagine someone convinced that someone is infected and decides to shoot them... This would be a psychological horror story I would love to read.