My uneducated understanding of the subject is that causality is one of the most sacred concepts in physics- any hypothesis that would require you to abandon it is considered highly suspect. But if I understand quantum physics correctly, anytime multiple possibilities are reduced to a single observation (like photons going through an interferometer) the outcome is utterly random- there is no way of saying why any one photon shows up in one exact location in an interference fringe, it just does. Doesn’t this eliminate the photon’s connection to it’s past?
What you are talking about is not causality, but determinism. Causality is indeed one of the most cherished principles of physics; it says that information, or influence, cannot spread outside the forward light cone. This implies that information cannot travel back in time (so that causes always precede effects), and also that physics is local (the evolution of a system depends only on its local surroundings). Determinism is the idea that the present state of the universe completely determines its future state. The “wavefunction collapse” postulate of QM reduces classical determinism to a probabilistic knowledge of the future (which was a major philosophical change from the clockwork universe sometimes imagined in classical-physics days, though probably not as staggering as loss of causality would be).
(Your particular example is causal, because the final state of the photon depends on the state of the system before the measurement, and not on what happens, say, tomorrow. It’s not deterministic, because the photon may be found at detector 1 with probability 0.6 and at detector 2 with probability 0.4.)
However, it is possible to formulate QM without the collapse postulate. This is basically what the many-worlds interpretation does, changing every “measurement” to a unitary interaction entangling the system and the observer, and making QM explicitly time-reversible. This preserves “determinism” for an isolated system, which is philosophically nice, though whenever you become an observer your branch of the wavefunction has probabilities associated with it the same as before.
In QM is Determinism consodered truly random? That is does the photon actually have an ability to maybe be at detector #1 or Detector #2 based on nothing more than some cosmic dice roll? Or are the photon’s chances at being in one or another place merely the limits of our ability to truly know all the effects on the photon and thus being able to predict with certainty where it will end up in the future?
In standard QM theory the outcome of a measurement is truly random, unlike the “randomness” in classical theories (like chaotic or thermodynamic systems) which is due to our insufficiently-precise knowledge of initial conditions.
This is disturbing enough to physicists that various “hidden-variable” theories have been investigated over the years, in which the photon has as a hidden part of its state the results of all measurements which might be made on it. A measurement result would then not actually be random; it merely appears that way because we are unable to see these hidden variables directly. (For example, you might postulate that for a pair of entangled photons, each individual photon “really” has a polarization, which you are simply unable to measure precisely.)
However, this turns out not to work; large classes of such hidden-variable theories (the “local” hidden-variable theories, in which the hidden variables are associated with each individual particle) are ruled out by Bell inequalities (QM, both theoretically and experimentally, violates Bell’s inequalities; local hidden variable theories do not). For a hidden-variable theory to agree with experiment, the hidden variables have to be “global”–associated with the system as a whole–which is much less appealing.
And here I thought you’d be among the last to support that rot. Many-Worlds is on the same philosophical level as solipsism, and still doesn’t respond to the OP’s question. To paraphrase and expand: “Is there any way I can predict what I will see?”, to which the M-Wer still has to say “no”, since there’s no way to predict which branch the questioner will travel.
To expand on this, quantum mechanical formulation allows you to have either determinism or causality, but not both. The standard Heisenberg formulation gives up determinism in order to keep causality (time-ordering is preserved, at the cost of having truly unknowable randomness). Global hidden-variable formulations are deterministic but are acausal (the global state tells you precisely what will happen, but “transmits” this information faster than light).
Because of relativity, most physics are strongly attached to causality and prefer the Heisenberg (or the equivalent Schroedinger) formulation.
I’m just going to chime in with a nitpick, that to me the phrase ‘utterly random’ has a very different meaning with the sort of probability functions that I associate with quantum physics. AIUI, QP is capable of making predictions on the order of ‘40% likely to be in this region, 25% likely to be in this region, 10% likely to be in this area, 5% likely to be in this zone…’ and so on.
“Utterly random” is more like, ‘well, it might be here, it might be in Albuquerque or orbiting the moons of jupiter. We can’t really tell.’ That is, there shouldn’t be certain known outcomes that are much more probable than others.
Hey, be nice. 
It’s called the many-worlds interpretation for a good reason: it makes exactly the same predictions as Copenhagen, so it’s precisely the same physical theory, and so of course the same probabilistic questions will arise for any real situation. (So you’re probably right that bringing it up was not terribly responsive to the OP.) But what MW does do is show that the “wavefunction collapse” can be thought of as arising from entanglement and not from an extra nonunitary interaction (which was always a bit of a problem in Copenhagen: when exactly does the measurement-with-collapse occur? and why can’t we pretend the measuring device is a quantum system and model its interaction unitarily? etc.). This makes “quantum eraser” experiments make more sense, since the “measurement result” that’s being erased is just another unitary interaction and not an irreversible projection operator.
It also means (I can’t remember who said this) that we can use quantum computers to enslave the inhabitants of parallel universes and make them do all our computations for us. 
We just need to figure out the Everett phone.