Well, and you can always stop eating red meats, right? If you're doing this specifically as a weight-loss effort, maybe it wouldn't be a bad idea to keep the chicken/turkey in your diet for the sake of protein... and just swear off red meats. No one's forcing you to go the whole 9 yards in either direction, right?
Chicken (as long as it's not battered and fried!) is a good, and healthy option! I don't eat wheat/gluten anymore because it doesn't affect my family's digestive system well.. and I'm dropping a lot of weight, still eating chicken breasts with rice and veggies all the time.