My Rav told me that my wife should try not to look at non-kosher animals when she’s pregnant. This precluded my ability to buy a dog or cat.
So I got a kid.
I believe this is a standard Lubavitch Shittah.
it is not assur to have a pet
doing so however is fraught with practical Halachic and Hashgufic problems
i dont know anyone who has a pet or would consider having one, its not even a remote consideration.
but for others, who are presently holding somewhere else, it certainly is not assur, but should not be entered into lightly.
I know of two cases of dog owners. One where the owner is blind, the other where there is a disabled child & the child’s Rosh Yeshiva suggested it.
In addition, many people own fish, where many of these halachas would apply as well.