For neutron shielding, you want low-Z material, not low density material. Neutron shields are pretty much always made of concrete, water, or high density polyethylene (HDPE). All of those are relatively high density (compared to a metal foam anyway). What all those have in common is a high density of hydrogen (concrete less so, but it's cheap so you can put more of it). Metal foam is low density, low hydrogen content, so pretty much the worst thing you could think of for neutron shielding.
And of course gamma and x-rays only differ in the frequency, but that means the energy, and more importantly the radiation length / penetration depth. The mm-thick layer of lead in the aprons they give you at the dentist will block x-rays, and low energy gamma rays, just fine, but they won't do anything to >MeV gammas that are the real problem with radioactive sources.
Also just in case you want to be pedantic, x-rays and gamma rays are labeled as such not just by energy, but by emission source. X-rays are generated by atomic de-excitation, while gammas are generated by nuclear processes, so there are actually some gamma rays with lower energy than some x-ray lines.