Soy.
1st - the reasons against Soy aren't nearly so cut and dry as the public seems to assume. Much of the conventional wisdom out there (on Soy, and many other topics) is simply wrong. I'd invite you to look at the CA Teacher's Study - one of the most robust and long term looks at human diets in my lifetime.
2nd - even if the human reasons against Soy were much more clear, and much more negative, there's still a bridge between eating soy yourself, and eating a creature (or its eggs) which has eaten soy. Much of what a chicken eats, during hte process of digestion, is broken down into different forms before being absorbed into the blood stream and distributed around the body - where it may (or may not) be concentrated in one organ or another. Some few things do make it intact, many others go right thru, excreted in the droppings.
To illustrate with a less maligned ingredient? Chickens, and their eggs, are gluten-free. I can link dozens of websites concerned with Celiac disease, including the Mayo Clinic, and more studies besides. The statement should raise no eyebrows, its well settled. and yet plenty of chickens eat wheat as part of their diet. Doesn't matter. Unless you are cutting open the crop and gizzard of a chicken recently fed wheat, or licking out its stomach, the glutens in wheat are denatured by the chicken's digestive system and no longer exist in that complex form when taken into the bird's bloodstream.
3) Ok, but why shouldn't I avoid it anyways, out of an (over) abundance of the precautionary principal? Because Chickens (particularly modern chickens) need an excellent diet in order to perform at optimum levels of growth, health, egg laying, etc.
Among the needs - things they can only get from their feed - is a critical (also called "limiting") amino acid called Methionine. Its called "critical" or "limiting" because chickens can only use protein up to the amount based on their Methionine intake - the rest is wasted. (There are others, with similar effect - Lysine, Threonine, Tryptophan are the top four, in descending order of importance). Plants, generally, do not offer "complete" proteins, the ratios of the critical amino acids are off. Its why conscientious vegetarians engage in protein complimentation with meals like black beans with yellow rice, in an effort to provide a meal which makes a complete protein in combination.
Plant sources of concentrated methionine are few and far between - so much so that synthetic methionine (appears as dl-Methionine on the ingredients list) can be added in very limited amounts (well below the current minimum recommendations) to feeds, EVEN ORGANIC FEEDS! Doing otherwise is the equivalent of sending ancient sailors on long sea voyages with no vitamin C source - only a lack of Met doesn't cause scurvy. Met is used in connective tissues, holding the whole body together - skin, feathers, tendons, the whole of the digestive tract, etc...
Soy meal happens to be an excellent source of Methionine, pound per pound. Its available at commercial scale, reasonably priced, and doesn't have some of the negatives of other high methionine sources (most others are very high fat, high fiber, or both - and high fiber diets aren't good for chickens the way they are good for us).
4) But why don't I feed my birds beans and rice, like a human vegetarian? you just said it makes a complete protein... Because beans don't provide enough methionine in their natural state to meat a bird's needs, much less when the total meal is made up of some small amount of beans (a moderate methionine source) together with a lot of rice (a low methionine source). To get the amount they need, they would have to eat a lot more. That brings a host of problems of its own - too many calories, too many anti-nutritive factors from the beans, etc
5) I still don't want to use Soy, because I heard soy contains phytoestrogens which are said to cause _____ by acting like human estrogen. First, go back to 1, above. Second, the plant based soy alternatives all include phytoestrogens too - including alfalfa, peanuts, clovers, and the beans mentioned in 4, above. and because they are mostly lower total protein sources, with different amino acid profiles, you generally have to use more of them, which can greatly reduce the differences in relative phytoestrogen contents between the ingredients. Beans are also high (as is wheat) in lectins, which bring their own concerns in a chicken's diet.
6) What are my other alternatives to highly processed soy/alfalfa/cottonseed/rapeseed/etc meals? Animal sources. Fish meal, Crab Meal, Porcine Blood Meal, etc. Certain yeasts (though expensive way to try and feed chickens).
7) No other way to get concentrated sources of methionine? Not off the grocery shelf. I'm starting to look at SAM-e, which you can get off the shelf (just as you can l-Lysine), but SAM-e and methionine are not the same in ways I can't yet describe, because I'm not done researching it and remain uncomfortable with my understanding of the ingredient. "S-adenosyl-L-methionine" by the way. Its close. Is it "close enough"? I don't yet know.
I think that answers most of the more common questions on the subject. Apologies for style, its "wierd" inside this brain. You got the [heavily edited] version.