Gurren Lagann

Gurren Lagann, known in Japan as Tengen Toppa Gurren Lagann (天元突破グレンラガン) is a 2007 science fiction anime series. It has since been adapted into manga and light novel forms.

Gurren Lagann and furry
For the most part, the furry characters in Gurren Lagann are antagonists known as "Beastmen" whose purpose is to eradicate humans. The Beastmen cannot reproduce, and instead, multiply solely via cloning.