Why doesn't the Whomping Willow attack animals?

Question

Both in the books and the movies, it has been shown on multiple occasions that the Whomping Willow attacks anyone within the range of its branches.

However, in HP:PoA I noticed that the tree didn't attack Sirius (in his dog-form) when he dragged Ron through the passage. From HP:PoA book,

Harry lunged forward, he seized a handful of the brute’s hair, but it was dragging Ron away as easily as though he were a rag doll —

Then, out of nowhere, something hit Harry so hard across the face he was knocked off his feet again. He heard Hermione shriek with pain and fall too. Harry groped for his wand, blinking blood out of his eyes — “Lumos!” he whispered.

The wandlight showed him the trunk of a thick tree; they had chased Scabbers into the shadow of the Whomping Willow and its branches were creaking as though in a high wind, whipping backward and forward to stop them going nearer.

Chapter 17. Cat, Rat and Dog

The tree went for Harry and paid no attention to Sirius.

And it has been mentioned that Padfoot, Wormtail and even Crookshanks were able to walk through and press the knot that froze the tree.

So, why doesn't the tree attack animals (or wizards in animal form)? Or was it grown only to attack humans/or keep humans away?

Answer 1

The Whomping Willow does attack animals as well. Here are a couple of relevant quotes (emphasis mine):

Crookshanks darted forward. He slithered between the battering branches like a snake and placed his front paws upon a knot on the trunk.
_{Harry Potter and the Prisoner of Azkaban, Chapter 17}

“They couldn’t keep me company as humans, so they kept me company as animals,” said Lupin. “A werewolf is only a danger to people. They sneaked out of the castle every month under James’s Invisibility Cloak. They transformed … Peter, as the smallest, could slip beneath the Willow’s attacking branches and touch the knot that freezes it. They would then slip down the tunnel and join me. Under their influence, I became less dangerous. My body was still wolfish, but my mind seemed to become less so while I was with them.”
_{Harry Potter and the Prisoner of Azkaban, Chapter 18}

As to why it ignored Sirius and attacked Harry, I'd go out on a limb and say Crookshanks helped him by pressing the knot long enough to carry Ron into the tunnel, since Sirius and Crookshanks had some level of friendship. Harry mentions it:

“He’s friends with that dog,” said Harry grimly. “I’ve seen them together.”
_{Harry Potter and the Prisoner of Azkaban, Chapter 17}

As does Sirius:

“It was a while before he trusted me. Finally, I managed to communicate to him what I was after, and he’s been helping me.”
_{Harry Potter and the Prisoner of Azkaban, Chapter 19}