Apart from gods and afterlives, do we apply the "logic" of "if I can't disprove it, it could exist"?

Do we? Yes. Should we? No. This type of thinking is called an appeal to solipsism. When applied to the concept of god or an afterlife it destroys its own premise. IE, if we cant know everything (or indeed can know nothing, depending on how far you take it) then we cant know anything about god or the afterlife, making any statement or claim to its existence null in an intellectually foolish attempt to permit it's existence.