Holographic measurements of the clustering of electrically charged, inertial particles in homogenous and isotropic turbulent flow reveal novel particle dynamics. When particles are identically charged, Coulomb repulsion introduces a length scale below which inertial clustering is suppressed such that the radial distribution function (RDF) mimics that of a nonideal gas. The result is described with a Fokker-Planck framework modeling inertial clustering as a diffusion-drift process modified to include Coulomb interaction. The peak in the RDF is well predicted by the balance between the particle terminal velocity under Coulomb repulsion and a time-averaged "drift" velocity obtained from the nonuniform sampling of fluid strain and rotation due to finite particle inertia. The resulting functional form of the RDF matches the measurements closely, providing support for the drift-diffusion description of particle clustering.