For me, it wasn't that a dog died. I'm generally okay with animal deaths in stories if they serve a purpose and aren't overly drawn out.
With Burn, though....
It was that the scene lingered on. It wasn't just "oh, the dog dies." You watch it get repeatedly stabbed with a fork while it's whimpering loudly in pain. To the film's credit, the tension leading up to the scene is actually done really well. You can see where it's heading, so you have a chance to brace yourself, but I still wasn't expecting it to be that gratuitous, either.
FWIW, I think many people overlook why there were so many complaints about the Depths of Fear dog. It wasn't just, "There's a dead dog." It was more like, "Why is there a dead dog here?" It seemed random and disconnected from the story the house was trying to tell. It also wasn't even killed by the Mouthbrooders. It died because a blast door closed on it. That made it feel even more contrived.
With Triplets, though, it makes sense. It's a house set in a suburban neighborhood, so of course there could be a family dog. Whether people like seeing it or not, it fits the setting and the narrative, which is why the backlash was basically nonexistent.