You left out another possibility beside many-world interpretation: our decisions may change the initial state of the universe. So, it's both: the universe is deterministic (in quantum mechanical sense), and we have a choice. Yep, quantum mechanics is even more counterintuitive than the usual particle-wave dualism and spooky action at a distance.

For technical details see "The Ghost in the Quantum Turing Machine" by Scott Aaronson.

Anyway, I don't think that peculiarities of the physical (and maybe also metaphysical) laws of our universe, which we certainly will not untangle in the near future, should play any role in AI rights question. More pragmatic approach should be taken, like constructing AIs who don't care for their own rights, but care for empowerment of humanity. Or something like that. Such that giving rights to AIs will not cause demise of the humanity.