We report a systematic magnetotransport study of superconducting infinite-layer nickelate thin films Nd$_{1-x}$Sr$_x$NiO$_2$ with $0.15 \leq x \leq 0.225$. By suppressing superconductivity with out-of-plane magnetic fields up to 37.5 T, we find that the normal state resistivity of Nd$_{1-x}$Sr$_x$NiO$_2$ is characterized by a crossover from a metallic $T^2$-behavior to an insulating log(1/$T$)-behavior for all $x$ except $x = 0.225$, at which the resistivity is predominantly metallic. The log(1/$T$)-behavior is found to be robust against magnetic fields, inconsistent with scenarios involving localization or Kondo scattering, and points to an anomalous insulating state possibly driven by strong correlations. In the metallic state, we find no evidence for non-Fermi-liquid behavior arising from proximity to a putative quantum critical point located inside the superconducting dome.