Did you notice that PETA defines "pet keeping" as the institution of
breeding animals as "pets", and that they contrast it with the phrase "animal companion"?
Here's the thing about PETA: PETA has never opposed people caring for animals in their home, just don't call them "pets". They really really really hate the word "pet" (note the scare quotes), which they consider
a derogatory term that undermines consideration for animal interests; they believe the entire concept of "buying" and "owning" animals like property harms animal welfare by creating millions of surplus unwanted animals; they believe that a "pet" is rarely regarded as part of the family, but essentially a toy that exists for a person's amusement and can be replaced with another "pet" at will.
I personally think PETA has a stick up their ass about the word "pet", but for 30 years they have vocally opposed the institution of
breeding "pets" (scare quotes!) for pet stores and puppy mills, when there are millions of homeless animals waiting to be adopted from shelters instead.
PETA has never objected to people adopting animal companions into their homes, only the practice of commerically breeding millions of animals as "pets".