Many times, the hybrids are infertile aren’t they?
Depends.
There is a relatively recent breed of feline, or domestic cat, called the Savannah Cat. It is a hybrid between a male Serval cat and a domestic kitty cat.
A good place to see the difficulty in breeding these cats is www.f1savannahcats.com, owned by Michelle Mills. Her male Serval cat, Falkor, will accept female cats to breed with who are not Serval like himself. The resultant kittens are not all fertile; the male kittens all being sterile.
Michelle Mills does a very good job explaining the facts on breeding Savannah Cats. I suggest if you are interested that you read the whole site. The photos of the cats/kittens are lovely.