Fish can generally inbreed without problems for a few generations, this is also one natural way that speciation occurs. The problem with inbreeding, not the ewww-it's his sister one, is that many organisms carry a certain number of detrimental or lethal genes that are recessive and more or less unique to a bloodline. So, naturally it's good to mix it up so these detrimental genes don't pop up. The same is true for some favorable traits, too, so it's a two way street. This is where the aesthetic traits like albinism, long fins, you name it, come up. They persist thanks to inbreeding.
One thing we do with fish all too often is use human cultural standards on them. Inbreeding happens all the time in nature and it's not nasty or illegal or anything like that.