[BaryonBundle]

The quoted example admits that it ignores strong fields and non-relativistic matter, which we have already established to be dealing with. The angular momentum of an element of volume in the neutron star likely contains enough kinetic energy to affect the Einstein field equations in a significant way. General relativity can't be ignored, but the Newtonian approximations has this habit of being nearly right more often than not.

I know that for rotating black holes the Kerr solution to the Einstein equations offers the best way to test these metric-based questions but I'm not sure if that's what you'd use for a Neutron Star.