food - Meat and mushroom allergies, why are they so rare?

There are a lot of food allergies, but for some reason not to meat (mammalian meat or poultry) or mushrooms. I've googled a bit, and now I know that one can actually have a meat or mushroom allergy, although the odds of that are very-very small. Why is it so?

Is it because both meat and mushrooms are usually cooked and that kills potential allergens? What about undercooked or raw food like portobellos or carpaccio and steaks? Or is it because animal tissues are so similar to ours and so are better digested? What about mushrooms then? Is it something else?

Also, are there any data of what types of meat and mushrooms are most allergic?