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We study the stability of the antiferromagnetic all-in--all-out state observed in dipolar-octupolar pyrochlores that have neodymium as the magnetic species. Different types of disorder are considered, either affecting the immediate environment of the Nd$^{3+}$ ion, or substituting it with a non-magnetic ion. Starting from the well studied Nd$_2$Zr$_2$O$_7$ compound, Ti substitution on the Zr site and dilution on the Nd magnetic site with La substitution are investigated. The recently discovered entropy stabilized compound NdMox, which exhibits a high degree of disorder on the non magnetic site is also studied. Using a range of experimental techniques, especially very low-temperature magnetization and neutron scattering, we show that the all-in--all-out state is very robust and withstands substitutional disorder up to large rates. From these measurements, we estimate the Hamiltonian parameters and discuss their evolution in the framework of the phase diagram of dipolar-octupolar pyrochlore magnets., Comment: 19 pages, 20 figures (main text: 12 pages, 13 figures)