Good points. The OPs first post made think of that and I intended to mention that mating related species will yield sterile offspring. Think mules. A cross between a horse and a donkey will beget a mule which is sterile. There have been crossings between chickens and some other galliformes. The offspring of those are also sterile - if they survive.
Hybrids are normally sterile. For simplicity I'd just agree hybrids are sterile. But there are cases of mules getting pregnant. Without looking it up now I don't know what the percentage of live births are or how long the young normally live. I know that many hybrids are not very thrifty, they either die before birth/hatch or shortly after. Some will make it a couple of years. Some species do fine and have a normal lifespan, it really depends on species and how closely related those two species are. I do find hybrids interesting, but for the most part I don't believe many of them should be purposely bred. In domestic animals it isn't such a big problem but you see a lot of intentional hybrids in exotics like parrots and snakes. Some of these species have no new (wild) blood being introduced into the captive population. Some snakes are hard to tell the hybrids from pure blood and those hybrids can breed and produce fertile offspring. It seems popular to hybridize macaws currently and laws prevent (for good reason) the capture of wild birds.
But now I'm going off topic so I'll stop there. It is a very in depth and interesting topic.