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Heimdall's eyes are naturally not pink. He is under Odin's loyalty curse. His eyes are pink like the Einherjar.

While the spell/curse is tied to Odin, Odin is also likely the only person who is able to dispell it. We also see in the game that even after the All-Father's death the Einherjar are still loyal.

(And also just like the Einherjar, his eyes go pitch black upon death, as the only way to break the spell was to die.)

This is why he cannot read Odin, and is so mindlessly devoted to Odin & Asgard unlike the rest of his family. He still has his living soul though unlike the Einherjar, its just being controlled. His shortsighted arrogance and inability to see the grander scheme of things could also have smth to do with this but thats just a game theory.

Hence Brok's comment;

Naturally, his eyes should look more like that of Bifrost Crystal. Like Mimir's eyes, or Týr's eyes:

But as we know, Mimir and Týr left Odin, and for good reason. Odin put the loyalty curse upon Heimdall for I imagine various reasons including making sure he stays. He's always going on about how useful Heimdall is to him. Not that he loves him, he's just a handy tool.

He also probably lied to Heimdall, saying something along the lines of how the spell would help calm and hone his senses and abilities. Keep him focused and sturdy. Which was likely half true, but, he had alternative motivations.

This is why Heimdall is so ride-or-die about Odin. His soul pretty much belongs to him. Even when Kratos was willing to spare Heim, there was no backing down. There was no giving up. Heimdall has been gaslit, manipulated, likely abused, and downright hypnotized into obeying Odin. Not for a second he will even think about the possibility of going against All-Father.