“At the other end of the spectrum, there are some ehrliche yidden who treat the petirah of a pet like a member of the family, even to the point of engaging in some kind of “levayah” for Lassie.”
I don’t question the ehrlichkeit of these people, but they are misguided. You wouldn’t have a funeral for your favorite recliner, no matter how much you loved it. In the same way, no matter how fond you may be of your pet, it is NOT a member of the family. It is not a person with a Neshama, and your relationship with it should be different in kind from your relationship with other people.
וע”ע משניות ברכות פרק ב משנה ז ובמפרשים שם