This is another area where they cannot seem to make up their minds. At one time, they banned cats because they thought cats carried demons. Now, they generally have no policy except the universal excuse for banning anything fun: "There is nothing wrong with it in of itself. However, our time is for the misery and is reduced." They also caution against treating pets as human, since they are going to die. (Yea, and so is Ted Jaracz. And yet he doesn't caution us against worshiping himself!)
Of course, this is subject to change. They could even now be working on a policy banning pets altogether, just so the people can have nothing enjoyable at all. You wouldn't want the people to get anything out of life apart from the boasting sessions and the field misery, now would you? Then again, Ted Jaracz could well join his buddy Albert Schroeder in hell before they have the chance to enact this policy (and I am using hell as a generic term for all punishment that is intended to last forever, including everlasting death with no one wanting them back as well as the hellfire--I am sure that, if we developed the technology to resurrect everyone, no one would want Albert Schroeder or Ted Jaracz back).