I'm also experiencing this issue in my game. Until yesterday, all pets were normal, but after I overwrote my save, they all turned pitch black. I tried creating new pets, and at first it seemed to work, but whenever I saved the game, closed it, and then reloaded the save, the same bug would appear on the new animals too.
I even tested older saves, and while the pets initially looked fine, the texture issue came back after reloading the save.
I'd like to know if continuing to play on this save could affect it permanently, even if a future update fixes the bug. I've already disabled mods, changed graphic settings, and tried various adjustments, but nothing has worked so far.
I really hope EA fixes this soon, because I just want to be happy playing The Sims again — and not become a mildly depressed young person without access to my virtual pets (that last part is said with irony, of course)