Its just an internet meme to “do not move the cat” while its sleeping, because its Anthropomorphism, becauae typically if you distrub a human baby, they’re gonna cry, so not disturbing them is a polite thing. So they’re extending this principle to pets.

Realistically, you can pick up a cat and move it somewhere and they won’t be bothered, they’ll just go back to sleep within 10 seconds. (Only applies to your cat tho, don’t touch a stray cat, they might bite)