I'm also wondering if it is worth to take the Shrine Token with you into the next life. Without knowing what it is for I did it now once, but it does not stack with another one found during the investigations, which makes it less inventory-effective, and sadly there was no ingame remark/comment on already having one of those in your bag.
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So the Shrine Token is the entrance key to a story dungeon that is not currently available (under the potion shop). Since it's not a difficult item to collect, I recommend not worrying about keeping it. There will be some hidden stuff if you go to the dungeon earlier than you should be allowed, so once the dungeon is in the game, keeping the token to use on day 1 of your next life would have value.