The SoCal Animal Defense League swarmed Kylie over the weekend in Bev Hills, slamming her and calling her a monster ... and now activist Rob Banks tells us the group targeted Kylie because she wears fur and was shopping at Moncler, which sells fox fur coats.

Those same activists tell us they will not stop going after Kylie until she swears off fur.

We're told Kylie's a target even if she's not wearing fur when protesters spot her ... animal rights activists are actively trying to hunt Kylie down, wherever she goes.

Meanwhile, honchos at PETA tell us the org would like to see Kylie join other members of her family, like Kim Kardashian, in embracing faux fur. The org says, "there's nothing uglier than stealing someone else's skin."

As you probably know, these poor animals are tortured ... often skinned alive. It's really awful.

PETA tells us they're encouraging Kylie to add Kylie Cosmetics to PETA's database of certified cruelty-free cosmetic companies ... even though Kylie Cosmetics already advertises they don't test products on animals.