The fact that the x-axis spin results are 50/50 strongly suggests something very specific and deterministic is going on. It would seem that we just aren't able to (pre)determine it without influencing it.
I agree that this flies in the face of everything that seems sensible in the world. I loathed quantum mechanics for years for reasons along these lines. Nevertheless, the universe is under no obligation to obey my intuition for what is sensible, nor my sense of elegance and beauty. Much to my disappointment, experiments make it absolutely clear that we do not live in a universe where "common sense" arguments are at all trustworthy on the scale of individual particles.
(Also, personally, I would say that the 50/50 result on the x-axis is purely a consequence of symmetry: nothing in the initial state or the measurement apparatus is set up to prefer +x over -x or vice versa, so it would be more or less impossible for it to split any way other than 50/50.)