My theory is that the sideways reality is caused by the fact that Sawyer, Juliet, Locke, Daniel, Miles and Charlotte did not time travel.
Things are very differen in the sideways reality. These changes seem to date very far back. For instance, Anthony Cooper does not seem to be a bad guy. So his life experiences must have been very different. So the changes can not be just attributed to Jacob's influence on thier lives.
I believe since 815 never crashed and the people mentioned above never came to the island, Daniel was not there to tell Richard and Ellie what to do with Jughead. The Others that were there in the 50s left the island for fear of the bomb. This huge change created a butterfly effect that changed the paths of many peoples lives.
The Dharma Initiative still came to the island, but there were no hostiles, so the had they island to themselves. Ben and his father came to the island and left. Then at some point, who knows when (70's, 80's 90's, 01, 02, 03, 04) either jughead exploded or a Dharma Experiment gone wrong sunk the island.