Why doesn't the invisibility cloak block spells?

Question

We know that when a curse hits an object, it bounces off/lights it on fire/makes it explode.

Another jet of green light flew from behind the silver shield. This time it was the one-armed centaur, galloping in front of Dumbledore, that took the blast and shattered into a hundred pieces

However, we see spells being cast through the invisibility cloak:

Sturgis had Moody’s Invisibility Cloak, right? So, what if he was standing guard by the door, invisible, and Malfoy heard him move - or guessed someone was there - or just did the Imperius Curse on the off-chance there’d be a guard there?

“Petrificus Totalus!” Without warning, Malfoy pointed his wand at Harry, who was instantly paralyzed. As though in slow motion, he toppled out of the luggage rack and fell, with an agonizing, floor-shaking crash, at Malfoy’s feet, the Invisibility Cloak trapped beneath him

He immobilized me, I couldn’t do anything, I was under the Invisibility Cloak

We also see Harry cast spells through the invisibility cloak:

Harry raised the hawthorn wand beneath the cloak, pointed it at the old goblin, and whispered, for the first time in his life, “Imperio!”

Hidden beneath the Invisibility Cloak, Harry cast a Shield Charm between Neville and Voldemort before the latter could raise his wand.

So why do the curses pass through the invisibility cloak? Even Xenophilius Lovegood explains how powerful the cloak is:

“Ah, but the Third Hallows is true Cloak of Invisibility, Miss Granger! I mean to say, it is not a traveling cloak imbued with a Disillusionment Charm, or carrying a Bedazzling Hex or else woven from Demiguise hair, which will hide one initially but fade with the years until it turns opaque. We are talking about a cloak that really and truly renders the wearer completely invisible, and endures eternally, giving constant and impenetrable concealment, no matter what spells are cast at it. How many cloaks have you ever seen like that, Miss Granger?”

Although he's talking about the cloak's strong concealment, we can still understand how powerful the cloak is, and that it has the ability to block spells. So why don't we see the cloak acting like that?

Answer 1

The Cloak Only Hides You From Death

Harry's cloak is very specifically not like most invisibility cloaks, so the one Moody has doesn't really enter into it. As for the other stuff... Magic is Weird. And specific. It hides you from death. Not other people. Or animals. Or spells. Just death. So in those instances where Harry's death could be the practical result of being revealed (such as when the Death Eaters attempt to summon his cloak when the group arrives at Hogsmeade in Book 7) it is totally unaffected. The Summoning charm isn't a "revealing" spell, but it's used in a revealing way where death might find Harry, so the cloak is immune to it. On the train with Draco, death was never going to be the outcome of "Petrificus Totalis" so it works. For the Imperius curse Harry uses at Gringots, we know some spells don't "deflect" and the Imperius curse is one of those. Going off the books/movies, only spells that are "beam" attacks like Stupify or the killing curse would have affected an article of clothing.

The Shield charm is iffy, as it has something of a beam but is an "area of effect" spell. I would argue that its creation point is based on where the user wants it and can see, so a normal cloth or even a glass window might not have been damaged by its casting. Of course, the other answer is that if the Shield charm would be blocked by a cloak in general, the likely effect would be the shield being created right there, knocking the cloak off. In this instance it would have revealed Harry, which could have gotten him killed. Which wouldn't have happened because it may have led to Harry's death, which the cloak's magic expressly prevents.

We know from other magical interactions that the intent/consequence of an action has an effect on the magic. (Harry surviving yet another killing curse in Book 7 being the main example.) The fact that nobody is ever hit by a life-threatening spell while under it is anecdotal evidence, but I admit not foolproof. Though an argument could be made that James and Lily survive being attacked by The Dark Lord three times while James has the cloak, but are killed the first time James encounters You Know Who without it. We don't know the specifics of the previous three attacks, but if James knew the cloak hides the wearer from Death, it seems likely that he would have been careful to have it on him/Lily at all times à la Harry in Book 6. Unfortunately for him he let his guard down once he has the Fidelius Charm in place, lets Dumbledore take a look, and pays for it with his life.

Answer 2

cloak that [...does things...] no matter what spells are cast at it

Note the "cast at it", not "cast at its wearer". It doesn't protect the wearer from any spells. I can't seem to remember any instance where it acted as a shield rather than light-bender. Still, no matter what spells you cast at the cloak, you won't be able to reduce its powers or maybe even change any of its properties. This is what's being told in the quote.

Moreover, what Xenophilius does is retelling a tale, and tales are not history: they get inaccuracies over time. Remember that Moody's magic eye can see through the cloak, so the concealment is not quite complete. The light does bend around, but special charms imbued into the Moody's eye can detect the cloak-wearer.