You are confusing classical physics (the orientation of the atom) with quantum mechanics (the spin of the atom).
The spin of the atom can only be +1 or -1, regardless of the coordinate system (i.e. orientation) you choose to measure it in.
It is comparable to the polarization of light. You can filter it in a certain direction, but it, too, is a quantum property. While light cannot pass through two 90deg rotated polarization filters. Ir can pass if you put a 45deg polarization filter between them. That can not be explained classically.
It is comparable to the polarization of light. You can filter it in a certain direction, but it, too, is a quantum property. While light cannot pass through two 90deg rotated polarization filters. Ir can pass if you put a 45deg polarization filter between them. That can not be explained classically.