The Mandela Effect isn't so much about our histories being false as it is about our memory about them not matching the recorded history in this realm, in which case, if our memories are accurate, and so is the recorded history here, the only explanation is a multiverse that allows for the transplanting of individuals between universes without them necessarily being aware of it, other than to have these strange experiences.
So it is possible that if you believe your memory is accurate, and so is the recorded history of this particular realm, then you may be one such transplant, along with myself and some not insignificant number of others. Have you ever had a period of missing time?