If they're in a free state, they can be distinguished. Consider Milliken's experiment and spacial separation. In systems, distinguishability depends on spin, as you were describing. A beam energy of electrons(Fermions) with net spin, is higher than a random spin beam. A polarized photon(Boson) beam has the same energy as an unpolarized one. That's the idea in your post.
On these threads it's common to find the belief that random processes have no cause, or that random is a cause. In this subthread, the former was the topic. Random refers to the process itself, is evidenced by the outcome and at any point in the process. If all processes in Nature weren't random, the probability of a real photon "hv" being absorbed by an harmonic oscillator would be zilch, because the linewith was zero and every trial would fail. ie. the tolerance is too tight.
True. I implicitly assumed free localized electrons with similar momenta when I made my statement (something I shouldn't have done).
Keep in mind though, that from a QM point of view, even unlocalized electrons are considered identical until a measurement is made, at which time they are placed into a position and/or momentum eigenstate (one of an infinite possible allowed number when in free space) - this imparted quantum "number" then gives a unique identity to the particle. You are right in this - free particles do not have discrete position/momenta spectra.
On these threads it's common to find the belief that random processes have no cause, or that random is a cause.
QM (Bell's inequality, etc.) only shows that random processes have no localized, physically measurable cause. It says nothing about globally hidden variables. (Then again, this starts getting us into the realm of the metaphysical and unmeasurable.)