I had similar concerns. There are some species of animal that can reproduce with their own offspring without affect. My grandfather's two donkeys turned into 22 and all were perfectly fine. Meanwhile, breed a dog with a sibling and you get mutations. I didn't know which way fish went so I built up my schools from different suppliers. I have ten emerald cory cats from five different purchases with five different origins. When I was buying guppy, I bought one at a time, to minimize the chance of purchasing direct siblings. Same with the Platy. My Danios came from the same place but my tank conditions are not ideal for their breeding and so I don't worry about them.
This brings up cross breeding. My dog is technically a Labrador, but ten generations ago the breeder was dissatisfied with the lines and the dogs being put out. He wanted a line of dogs for a very specific purpose with very specific traits, including size, temperment, muscle mass, etc. He bred into the line some other breeds of dog to create the traits he wanted as opposed to inbreeding his dogs that already had those traits. It took over thirty mated pairings of labrador X dogs of different lineages, and six generations to generate the specimen he was looking for. Those dogs were then bred into other pure labs and each other. After this many generations they are technically again Labradors. By all appearances they look it. With a few exceptions. His dogs are taller, more muscular, have higher endurance, a very true work ethic, and some distinctly non Labrador personality traits. The bonus is they are genetically superior, without the allergies, hip and joint problems, and the poor temperments of their contemporaries that have been inbred to the exclusion of common sense. His lines are champions in the field and are used across the US by law enforcement and private firms for all manner of detection work, police work (yes, labradors with Shutzhund training), and by many private owners for field and agility.
Anyhow, I think where I was going with this it, even the purest of fish will diminish over time without new blood. Without the availability of non familial new blood, the next option is cross breeding with other species and then selectively breeding the offspring back into the original line. This creates enough new genetic material to carry on the original breed without diminishing their desired traits, the same way inbreeding would.