In hybrid cichlid males, they are usually infertile. Flowerhorns i don't know why most of them are fertile(maybe breeding the few males that were found to be fertile?). I think inbreeding decreases the chance of being fertile and so does being a hybrid(I don't mean hybrids that have been crossed with fish in the same genus). And not all hybrids are infertile, for some animals most of the hybrids of them are fertile.
I assume you mean between two different genus...there are tons of cross's that are indeed fertile.
I do get what your saying fishfreak95...many of the new domestic X wild cat hybrids suffer from infertility in the f1 males. This is because they aren't quite compatible genetically (different number of chromosomes I think) not because they were inbred.
Maybe breeding outside the genus reduces fertility. Most flowerhorn have more Amphilophus in them than anything else. Blood parrots more than likely have Amphilophus and Veija in them.