Again: where is the forcing?
They are ASKING people to donate their pets corpses. That is so far removed from forcing, I don't know how to explain it, if you think that is forcing people to do something.
If somebody asks for something, you are free to NOT do that thing. But those who want to not just put their pets in the ground, can use the offer.
And regarding "not part of our culture": you know that the act of putting cat babies in a sack and drowning them, because you couldn't care for all of them, isn't out of style that long, right? So that shows you 3 things: caring for pets means different things for different people, not everybody is opposed to killing pets and lastly: cultures change.