My cat isn't allergic, but she just doesn't like red meat. I bought fresh lambs heart and pork heart but she refused it. I decided to cook it a little to see if she changed her mind, and she would bite into it then spit it out, and abandon the rest. If I leave down beef mince she will pick at it reluctantly. And she completely turns her nose up at raw steak (not that I planned to feed her steak, I just cut a bit of my own off before I cooked it to see what she would do). She will eat pork liver, and would eat pork liver all day everyday if I let her. So when I blend it with beef kidney in the blender, she likes this mixture too. With all (boneless) poultry and turkey products, she can't get enough of the stuff.
I think they just have preferences like humans. Provided they eat a balanced raw diet of whichever animal(s), they will do a heck of a lot better than cats raised on commercial muck.