Neural physics certainly is pure magic but so are many other things really:
FTL, anti-gravity, non-rotational/non-mass artificial gravity, extended guided/shaped magnetic fields, hard light, possibly UNSC fusion engine effectiveness*, the Flood's apparent telepathy (though it could be part of the neural physics). At least.
Anti-gravity may be possible, at least apparent anti-gravity (such as the EmDrive which seems to work even though it should not based on our current understanding, or the apparent acceleration of universe's expansion) but the way Halo portrays it is unlikely.
Magnetic fields can be manipulated but they can't be arbitrarily extended and guided, if they could be, it would be useful and actually allow plasma weapons the Covies have (though there would be no point, just use a frigging particle beam, it is the same but faster).
*given the apparent lack of massive amounts of propellant, they have to be super-super efficient, especially since the books (Nylund's mind you) imply human ships can travel very fast in-system (and such acceleration requires inertial dampening by the way, which is yet another magical system, at least the way it works in Halo), and this makes them pretty much pure magic due to various required secondary things to make them work in reality that probably don't exist in Haloverse since they would affect other things so much but we don't see them.
EDIT i have nothing against magic in "scifi" as long as it is utilized to its fullest extent. Unfortunately Halo does not do this...
I only just got home so I'm afraid I missed all the stuff from today, must try catch up somehow.