Optical fibers have unwanted residual birefringence due to imperfections in fabrication processes and environmental conditions. This birefringence will randomize the state of polarization of propagating signals and may harm the performance of four-wave mixing based processing devices. Here, we present a quantitative study of the effects of birefringence in orthogonal-pump four-wave mixing systems, and identify different regions of operation of the optical fiber, mainly determined by the relative magnitude between the physical length L and beat length Lb. This finding clarifies the characteristics of the complex interplay between birefringence and four-wave mixing and advises appropriate fiber length selection for minimized polarization dependent gain.