I "think" what you mean is that the causal mechanism (such as it is, what you can control) essentially ENDS when the 2 photon entangled state begins. Because there is no known root cause (in any theory I know of) that explains* what the entangled outcomes would be for the various possible observations. In other words: you might be able to create the entanglement initially, but what happens "next" cannot be considered causal or deterministic via the formalism. And I naturally agree with that view, if I am close to what you mean.Of course the formalism does not supply a causal mechanism for the correlations in the sense you seem to imply (but not explicitly mention to keep all this in a mystery ;-)), because there is no causal mechanism. The causal mechanism is the preparation procedure...
And you have then said that "leads to a two-photon state, where both the momenta and the polarization of these photons are necessarily entangled." And you agree that 2 photon state is not classical, so we are in good agreement to this point. The only gap remaining is acknowledging that whatever happens next is an example of a) apparent randomness; and b) quantum nonlocality, things which MUST be present/embedded in any theoretical framework - even if to say the mechanism is unknown currently. We don't know a) why you get spin up, for example (or any value of a measurement on an entangled basis). And we don't know how the system evolves from a 2-photon state (spin/polarization undefined) to 2 matching 1-photon pure states whose distance/separation precludes influences limited by the light cone defined by a measurement.
You don't see a) and b) as mysteries, OK. We can agree that mysteries are in the eye of the beholder.
*Even in MWI there is no explanation of why we see a particular outcome; and in BM there is no possibility of observing the pilot wave that guides a particular measurement outcome.