We exploit the anisotropic plasmonic behavior of gold nanorods (AuNRs) to obtain a waveguide with a nonlinear coefficient dependent on both the frequency and polarization of incident light. The optical properties of the waveguide are described by an extension of the Maxwell Garnett model to nonlinear optics and anisotropic nanoparticles. Then, we perform a study of modulation instability (MI) in this system by resorting to the recently introduced photon-conserving nonlinear Schrödinger equation (pcNLSE), as the pcNLSE allows us to model propagation in nonlinear waveguides of arbitrary sign and frequency dependence of the nonlinear coefficient. Results show that the anisotropy of the nanorods leads to two well-differentiated MI regimes, a feature that may find applications in all-optical devices.