Why wasn't the Imperial Pilot in Rogue One made insane or affected?

Official Novelization by Alexander Freed covers this.

1. Mind effects aren't an ironclad rule. The word used is "tends to".

   “The unfortunate side effect,” the ghost voice of Saw Gerrera said, “is that one tends to lose one’s mind.”

2. Bodhi was affected, for a while.

   “Galen Erso,” Cassian tried. He meant to sound gentle, but he heard urgency slip into his voice. “You know that name?”
   The man hissed, turned his cheek as if he’d been slapped. His breath picked up, swift and loud like a hound’s panting....
   The man opened his eyes again. His breathing slowed. “I brought the message,” he said. “I’m the pilot.”
   Then, in surprise and horror and hope: “I’m the pilot. I’m the pilot.”
   (Chapter 6)

   The pilot refused to look directly at Cassian. They’d gone around twice already, Cassian asking questions and the broken man answering in jumbled words and mumbles. There were hints of insight to be found—Cassian had heard the words planet killer more than once—but little else... (Chapter 8)

3. Then, we see exactly what the effects on his mind were.

   He didn't quite lose his mind in a conventional sense, he had confusion between past and present - the way it sounds like to me, short and long term memory. That isn't really a permanent thing, as eventually all that settles into long term memory again.

   Bodhi Rook understood the distinction between past and present, between recollection and reality; he just wasn’t sure which was which anymore.
   Bor Gullet had taken everything Bodhi was—every intimate thought and dream, every cherished or forsaken memory—and torn through it with tendrils like scalpels. A scrap of first kiss drifted, ripped and sodden, into a pile on the right; a ribbon of kyber crystals floated to the pile on the left, pressed and preserved for further examination.
   When Bor Gullet and Saw had completed their investigation, Bodhi had tried to stuff every memory back into his mind. He was certain they hadn’t all fit quite right.
   “I’m the pilot!”
   Who had he said that to? Someone had listened to him at last. Or was that a memory from long ago?
   Was he still in the cage with Bor Gullet?
   No. But he was in another cage. It smelled of his own putrid scent. His flight suit chafed his icy flesh, irritated his sores, and ground dirt into his wounds. The whole world was rumbling like a ship taking flight. Surely that, Bodhi thought, was a memory?
   Panic helped Bodhi find words. “Wait!” he cried. “No…”
   ...
   “Come on!” the second man called. His name is Chirrut. “Let’s go!”
   Was this reality?
   Was this a rescue?

   ...

   Realizations crashed together. Bodhi was on Jedha, had never left Jedha, and he was looking onto the valley where the Holy City had been. And above him, in the sky…
   “No,” he whispered. “No.”
   This was not a rescue. This was a trick of Bor Gullet. This was the reason he had left the Empire, abandoned his friends, trusted the words of Galen Erso, suffered torment and humiliation—to stop the battle station, stop the planet killer from coming to life. What he saw was not real. It could not be. “It wasn’t supposed to happen yet,” he whispered, though no one listened.

4. Looks like typical mental health techniques (inadvertently) helped him, same ones used on amnesiacs in real life; such as introduction to the familiar.

   The cabin lurched and swayed. Baze, Chirrut, and the woman clutched at the seats, at support struts, to keep from being dashed against the walls. But even with the floor unsteady beneath him, even with the metallic wail of the wind against the bulkhead, Bodhi felt comforted. He was on a ship now. He knew ships.
   The hull shrieked as something heavy bounced off the top of the U-wing. The deck dropped, sent Bodhi onto his hands and knees and drove spikes of pain into his wrists. He went sliding as the ship banked. He recognized the sound of the engine (an Incom Corporation rebuild of their 9XR standby…) as it strained against the storm.
   He understood that Bor Gullet was gone from his mind. Yet the memory that seized him was every bit as vivid as those the creature had evinced. Bodhi looked out the viewport and saw, instead of the dust storm, the emerald and turquoise hues of titanic gas clouds. Lightning volleys like alien dancers leapt from one cloud to the next, causing each to ignite and burst. Bodhi was laughing as his shuttle, a Nu-class transport barely viable for training runs, bounced and twirled, and his classmates cheered him on…
   It was a memory of utter serenity. Then his flight through the gas giant of Bamayar IX was over and he was gazing into the dust storm again as darkness closed around the U-wing.