The reason you have heard such mixed answers to this question is that while pigeons and chickens can be mixed there are several "rules" if you will, that must be observed for it to be successful. The people who have said t will work are probably (whether knowing or unknowingly) following these, while those who haven't have seen first hand how badly it can go wrong if you mix them in the wrong way. So basically here is the "list":
#1 You can only house pigeons that fly well with chickens. Breeds like homers, rollers, high-flyers and ferals should be fine. Fancy or heavy breeds that don't fly well (Fantails, Trumpeters, Giant Runts, Croppers, Jacobin, etc) won't work. They will get picked on or killed by the chickens. Some fancy breeds that fly better (Tumblers, Ice, Swallows, Monks, Starling, etc) may work but it would depend upon the individual pigeons and chickens. Play it safe and don't house those breeds together unless you have a back up if it fails.
#2 Don't put young pigeons who can't fly well yet with chickens and never let pigeons have babies where chickens can get at them. Either don't let pigeons breed that live with chickens, shut them in a breeding box, or give them an enclosed nestbox/hutch with some type of trap/high entrance only the pigeons can get in. Chickens will kill helpless babies.
#3 Have plenty of perches, food, and water. Put some perches high enough chickens can't reach them or at least high enough they won't use them much. While pigeons can do well on chicken pellets you would have to have to have plenty available or else if you are going to feed pigeons grain it will have to be fed up high or somewhere else the chickens can't steal it.
All in all it is usually easier to just house pigeons separately, but in some cases it may be worth keeping them together. In my case, I live in the city and have a very tiny yard. Between my chicken coop and run and my fancy/breeding pigeon loft literally 1/4 of my yard is taken up. I do not have room to add another pigeon loft which is what I would do if I lived in the county. So I keep my flying pigeons (mostly homers and homerXs) with my chickens. But they have a small area only they can get into with their own food and water. They spend more of their time out in the chicken run or even inside the chicken coop (there are perches all over) but if they want to they have a place they can get away from the chickens. In my situation it works well.