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You'll come to appreciate the elegant beauty of «shift» soon enough.
The result is that both Butt and Cake move in the direction the other is facing. If they are both facing up, then Butt and Cake both move one space up, ending up layered again for the next move. If Cake is facing Left and Butt is facing Right, then the Cake will move right (Butt shifts it) and the Butt will move left (Cake shifts it). For the latter situation, Tree would not move at all since it gets told to shift both one left and one right, for a net movement of zero.
Note that once an object shifts, it turns in the direction it has been shifted. The aforementioned illogical "Butt left, Cake right" will result in a Butt that is facing left and a Cake that is facing right, despite the fact they were facing the opposite directions on the previous move.
Baba is you, is renowned for having very little turn order. For the most part, it tries to get instances of the same rule to operate simultaneously. On top of this, the game doesn't really follow the laws of physics, nor does it directly explain what any rules do for you to be able to nitpick the fine print.
Because of this, shift works in a simultaneous-like manner, where both Butt and Cake would simultaneously move each other to the next square, assuming they're pointing in the same direction.
If it didn't, it would fall out of line with the simultaneous-like nature of other rules and puzzles around doing two things simultaneously. IIRC, there is even an infinite loop that the game acknowledges because it doesn't want to decide on turn order or priority.
Throughout the game, the later you go, your assumptions are constantly challenged in somewhat weird ways until you accept that the game as a whole is weird.
Don't worry, you can quickly develop a feel for what the game's actual logic is. I didn't look up any guides and by the end, I could categorise all of the laws in order to beat the rest of the game smoothly.