Do non neutered cats shed more hair?

In my experience, cats shed the same amount of fur after they are spayed/neutered.

I have had cats that have been unneutered and unspayed and I have not seen any difference in the amount of shedding after they have been spayed/neutered. Not even when the cats have been exposed to the stress of getting a new home where another cat was living.

Cats do normally shed some fur all the time, but the amount of shedding does increase in the spring when the days are getting longer, and again when the winter comes and the days are getting shorter.

This does happen in both indoor and outdoor cats, so it is controlled by the duration of daylight hours.

Cats can lose fur as a result of stress, but this is more pronounced if the cat starts over-grooming itself, or as a result of illness.

You do mention your cat starts to shed more fur after changing the type of food you give your cat, and it is possible the composition of the new food can induce more shedding simply because it contains nutrients your cat has been in short supply of. If this is the case, your cat will soon be back to shedding normally again.