So /tg/ I did two games with different settings and systems, but using the same ideas. They were Delta Green and Chronicles of Darkess (which we later changed to Hunter the Vigil and Vampire).

The concept was to make a chronicle inspired by Twin Peaks but using that "Mandela Effect" conspiracy theory. I'll try to summarize months of sessions. The players had to go to a small town in Maine called Honeyville and discover who killed the daughter of the CEO of a mega-corporation. They discover that not only does a cult that worships a spiritual creature with Lovecratian elements, called "Mr. Nobody," control the town, but also the corporation (something like Pentex from Werewolf: The Apocalypse).
The cult is having a "civil war," and one of the factions sacrificed the CEO's daughter without the approval of all the members.

Where does the Mandela Effect come in?

Well, both players and cultists learn to enter a shadow world, a temporary reality far less detailed than ours, but similar to the Umbra or the otherworld in Silent Hill. Every time someone enters this world and interacts with anything there (even opening a door counts), it affects our reality. The world's history changes, people disappear or are replaced, and the memories of those who didn't enter this world also change. People who manage to enter this world are called "jumpers."

So, both players and NPCs caused changes and only realized it when it was too late. It was amusing to see the confused faces every time they returned to town and realized something had changed.
In the end, the players prevented the cult from sacrificing an albino girl with Rh-null blood, the rarest blood type in the world. The ritual would have made the spirit become a full-fledged god.

Oh yeah, and the NPC that summoned the player characters was basically David Lynch, so I had to constantly imitate him.