This question is mostly about a strange seeming similarity that I've noticed between the nature of the weak force and the nature of black holes, which seems to imply that even some astrophysical black holes might be able to interact significantly with the weak force:
Only left-chiral fermions and right-chiral antifermions participate in weak interaction. Even though I know that "spin" or "quantum angular momentum" is not actually believed to involve particles spinning on their axes, I have heard people say that it "really is" angular momentum. As I understand it, the justification for this claim comes primarily from the fact that electrically charged particles with spin create magnetic fields in the same way that they would if they were literally spinning (more-or-less, at least). (I suppose this might also apply to any affects relating to the nuclear strong or weak forces that spinning would cause, though I don't know anything about that.)
Moreover, the quantities of "weak isospin" and "weak hypercharge", which apparently are important for describing how particles interact with the weak force, are related to spin, chirality, and electric charge.
The explanation that I heard of why the weak force is weak (from Don Lincoln) is that it is because the virtual W and Z bosons that "mediate" it have average masses that are very high — far higher than the mass of most elementary particles. This means that the only way that most elementary particles can emit one of these particles is if they the emit one which randomly has an extremely small mass for the short amount of time that it exists, as allowed by the Heisenberg Uncertainty Principle. One thing that this explanation implies is that the weak force is stronger for elementary particles that have higher masses, at least until that mass becomes higher than any of the likely masses for W and Z bosons, and, in fact, the weak force is apparently the strongest force for top quarks, which is why they decay so quickly.
Thus we have that the weak interaction of elementary particles (and I'm not sure if it really is just elementary ones; that's just all I've definitively heard about) is determined by the "mass", "angular momentum", and electric charge of those particles. By strange coincidence, "mass", "angular momentum", and electric charge are exactly the properties that black holes can have according to the "No Hair Theorem". This is the primary impetus for my question: "Can black holes interact with the weak force?"
It seems to me that the fundamental question being asked here is whether the "mass" and "angular momentum" are really somehow the same in both cases. (It seems quite likely to me that they are not, which would tend to doom this idea of black holes acting like elementary particles.)
There are also a few other things that must be considered to fully answer the title question:
If we come to the conclusion that the "angular momentum" that matters for weak interaction is fundamentally different than the frame-dragging "angular momentum" of black holes, then we still have to contend with the fact that lots of left-chiral fermions fell into the black hole, so one might expect the spin to add up like it does in baryons, atoms, etc., (unless, of course, nothing ever falls into a black hole in a way that is meaningful to outside observers, and everything is effectively just sitting there ridiculously time-dilated on the black hole's surface).
This is really just part of the question of how the No Hair Theorem combines with Quantum Field Theory. It seems to me that, according to QFT, all quantum fields should extend out infinitely across space, just like the electromagnetic and gravitational fields. The only differences being that some (particularly color charge) are always pretty completely canceled out by other charges over any non-tiny distance, and others (like the weak force and nuclear force) fall off at a much faster rate than the inverse square law of electrical and gravitational forces over long distances, but crucially never become zero.
These differences make the question of interaction seem pretty esoteric for any macroscopic black hole, since their effects would always be so ridiculously small, but they might matter for micro-black-holes and they might even be related to how information could be imprinted on the surface black holes to avoid the Information "Paradox".
Here are a couple of Stack Exchange questions I found that are specifically about how QFT interacts with the No Hair Theorem: Black Holes and QED , No hair theorem for black holes and the baryon number
There's also the question of whether W and Z bosons could possibly appear as part of Hawking radiation, as well as the question of whether something to do with electroweak theory could make black holes interact with the weak force if they were very small or in very hot environments or formed in a specific way or something.
For reference: I'm fairly familiar with calculus, somewhat familiar with linear algebra, and less familiar with group theory and topology, but most of what I know about physics (and, indeed, about math beyond calculus) comes from YouTube, Wikipedia, and various pop-sci materials.