I suspect, although I've never had an opportunity to test this, that halos in an isotropic host material would be non-pleochroic, unless the radiation damage itself caused some local anisotropy. But I also can't think offhand of an isotropic mineral where I've ever seen halos, even in other ferro-magnesian silicates like garnet that might seem like prime candidates?  I suppose for an alternative test, a sample containing a halo-susceptible mineral such as the cordierite in my video could be sectioned so one of the optic axes of the cordierite was perpendicular to the stage, and then searched for halos.  If seen, I would guess these halos would be at best minimally pleochroic, or perhaps even entirely non-pleochroic?  Or maybe not?

But maybe also, they might not even be seen at all?  Apparent from the video is that there is a particular grain orientation where the halos practically disappear; if that orientation just happens to be Y parallel to the lower polarizer (I've never tested this, so I don't know), then one would never see any halos in a cordierite oriented to give a centered optic axis figure (where all rotations would show Y), even if those halos would be abundantly obvious in a different orientation.  I'm sure someone must have tried this before... probably back in the 1800s.

I also wonder that the actual pleochroism effect may be less noticeable in a sheet silicate like biotite (compared to cordierite), because I suspect the halos are most readily observed when the cleavages are in the plane of the thin section (in fact, I can't recall seeing halos in biotite grains oriented differently, even in the same samples where other grains do show halos.)  In any case, when the cleavage is parallel to the plane of the thin section, this orientation is almost looking straight down the optic axis of a low 2V° mineral like biotite. As speculated above with the cordierite, in a near-isotropic orientation, perhaps pleochroic halos just aren't pleochroic??

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But all other crystal systems are permissive to pleochroism. So "pleochroism" in halos would seem to be the rule rather than the exception. It's also possible they were named "pleochroic" halos well before radiation was even a known or well-understood phenomenon?

Yes, I believe that is the prevailing theory for blue/purple in halite, but above I was referring more specifically to halos around radioactive inclusions, which I wouldn't have typically expected to be present given how halite forms.

But, in wanting to add some color to my answer (heh heh), I ran across an interesting paper where the authors not only did observe haloed and "anti-haloed" inclusions in halite (so the latter a bit like my bleached anti-halos in Norra Kärr fluorite) in some Polish halite, typically of a potassium-bearing (hence K-40 bearing) mineral like sylvite or carnallite, but also observed local optical anisotropy in the halite. While the anisotropy was presumably related to stress, it still made me wonder (and the authors didn't indicate) whether the blue/purple areas that were of lower symmetry were also pleochroic... (salty) food for thought.