Why do my cats keep bringing me things to my house door when I sleep?

Solution 1:

Because it's their intended behaviour.

When the player sleeps, tamed cats move toward their owner and sleep near them. There is a 70% chance for a tamed cat to give the player a gift after they wake up, but only if the player sleeps at night. If a player has multiple standing tamed cats in the area, only the tamed cat that sleeps on the player may provide a gift.

This is what items you can get:

More information here.

Solution 2:

This is just an easter egg Mojang put into the game so that Minecraft cats brought dead animals to you. In particular, the phantom membranes are very useful because you can use them for potions of slow falling and to repair an elytra.

Phantom- Phantom membrane

Zombie- Rotten flesh

Rabbit- Rabbit feet, Cooked rabbit meat, Rabbit hide

Chicken- Feather