One-atom-thick rare-earth/noble metal (RE-NM) compounds are attractive materials to investigate two-dimensional magnetism, since they are easy to synthesize into a common RE-NM2 structure with high crystal perfection. Here we perform a comparative study of the GdAu2, HoAu2, and YbAu2 monolayer compounds grown on Au(111). We find the same atomic lattice quality and moiré superlattice periodicity in the three cases, but different electronic properties and magnetism. The YbAu2 monolayer reveals the characteristic electronic signatures of a mixed-valence configuration in the Yb atom. In contrast, GdAu2 and HoAu2 show the trivalent character of the rare-earth and ferromagnetic transitions below 22 K. Yet, the GdAu2 monolayer has an in-plane magnetic easy-axis, versus the out-of-plane one in HoAu2. The electronic bands of the two trivalent compounds are very similar, while the divalent YbAu2 monolayer exhibits different band features. In the latter, a strong 4f-5d hybridization is manifested in neatly resolved avoided crossings near the Fermi level. First principles theory points to a residual presence of empty 4f states, explaining the fluctuating valence of Yb in the YbAu2 monolayer.