Wouldn't the neutron flux mess with the properties of the nuclear payload? Shielding against a neutron flux from nuclear explosion probably not practical given the sizes warheads.

Light atoms are used to slow down fast neutrons. Thermal neutron absorbers (large neutron capture cross section) like boron, lithium or cadmium is used for shielding.

Li6H is perfect for shielding warhead. Li6H (Lithium-6 hydride) contains hydrogen to slow down neutrons and lithium to absorb them. It has hightest hydrogen content of any hydride, high melting point and can be casted.

The shielding takes some space and the warhead yield is smaller than without shielding. The goal is not to completely block neutron flux but to reduce it to the level where exploding countermeasure must be very close.

If I recall correctly the case of the re-entry vehicle tends to be stuff like depleted uranium, which is pretty good protection against neutron flux up until the point where it begins significant breeder contributions. You'd basically have the hit the vehicle anyway to get close enough for that.

Uranium or lead, heavy nuclei that shield well against gamma radiation would do little for neutrons.

Neutrons needs something with light atom like hydrogen - water or maybe polyethylene and lots of it to slow down. So a small nuclear explosion which emits a neutron pulse might work pretty well. It would hellish if it somehow exploded over a population center, though. Didn't get hit by the ICBM (good). Everyone's bones melted (bad).