Pigs are People!

(...and people are pigs.)

Pigs are People is a religion as revealed by Justin Roiland.

The basis of the religion is when a person dies they are reincarnated as a pig. When a pig dies they are reincarnated as a person.

Ideology
When either a pig or a person dies, you are sent to a horrible place called "The In-Between Lives" area where you fight and scramble a random pig zygote. Your memories from your former life are erased and you exist simply as a soul. This place is apparently extremely painful. In order to get out of this In-Between Lives area, you must be reincarnated in the opposite form (if one was a pig in the former life, you'll become a human and vice versa).

The 24 Hour Window
The reincarnation occurs within 24 hours from the time you died. But you pig body may not always be from your time for instance, if you die Today you will be reborn in a random time within a span of 200 years, 100 years forward or 100 years back.

Oh, and...
It's a possibility that you could come back as a pig or as a person on another planet (as long as there are pigs and people there).

A soul cannot be in the same body twice.