I bought a Solar Eclipse Lupora, she and most of the others for sale were declared infertile for some reason. I also looked at some Qitari with the same issues. Could someone please explain how infertility works on this site? (It's not inbreeding, the Qitari were at 0)

Infertility means a pet cannot breed. Pets can be "inferted" with an Exceptional Infertility Kit, available from the diamond shop. It's usually used for project pets and max/super stat pets, so no one can breed more and make a profit off of someone else's hard work.

Theres no genetic component. Players can use an item to make their own pets infertile. This is usually done to offspring of breeding projects so that those who buy the pets dont get an easy pass to making money. Breeding projects, especially things like max stats, take a lot of time and money to complete and breededs dont want others to start their own projects using their completed pets.