Given that both Albus Dumbledore and Severus Snape could read minds, how did Remus Lupin conceal his knowledge of the fact that Sirius Black was an unregistered Animagus? This seems especially odd given Snape's stated suspicion of him.
Dumbledore trusted Lupin. And Snape trusted Dumbledore.
As the following conversation shows, Snape suspected Lupin of helping Sirius but Dumbledore trusted him. Snape tried to persuade Dumbledore that Lupin presented a security risk but was loyal enough to Dumbledore not to interrogate Lupin himself.
“Have you any theory as to how he got in, Professor?” asked Snape.
Harry raised his head very slightly off his arms to free his other ear.
“Many, Severus, each of them as unlikely as the next.”
Harry opened his eyes a fraction and squinted up to where they stood; Dumbledore’s back was to him, but he could see Percy’s face, rapt with attention, and Snape’s profile, which looked angry.
“You remember the conversation we had, Headmaster, just before - ah - the start of term?” said Snape, who was barely opening his lips, as though trying to block Percy out of the conversation.
“I do, Severus,” said Dumbledore, and there was something like warning in his voice.
“It seems - almost impossible - that Black could have entered the school without inside help. I did express my concerns when you appointed-”
“I do not believe a single person inside this castle would have helped Black enter it,” said Dumbledore, and his tone made it so clear that the subject was closed that Snape didn’t reply.
(Prisoner of Azkaban, Chapter 9, Grim Defeat).
Legilimency is considered a highly invasive and none-too-subtle form of magic. You can tell when you're being Legilimens-ed. Voldemort did it to his followers all the time; it was normal practice and they couldn't really do anything to protest.
"Saturday...at nightfall," repeated Voldemort. His red eyes fastened upon Snape's black ones with such intensity that some of the watchers turned away, apparently fearful that they themselves would be scorched by the ferocity of the gaze. Snape, however, looked calmly back into Voldemort's face and, after a moment or two, Voldemort's lipless mouth curved into something like a smile.
(Deathly Hallows, Chapter 1, The Dark Lord Ascending).
Dumbledore is somewhat more considerate towards his own followers/staff. Lupin was not only a valued member of staff but an old friend that Dumbledore had known as a student and as a member of the original Order of the Phoenix. Invading his mind and reading his thoughts would've been a betrayal of trust. Lupin would've been offended and the relationship would've been difficult to salvage, even if Dumbledore gained some useful information. Regardless, as the quotation above shows, Dumbledore didn't suspect Lupin so wouldn't have been inclined to use Legilimency anyway.