Photonic and electronic-photonic hybrid devices hold great innovation potential, offering significant advantages over traditional electronics. Remarkably, transmission efficiency is boosted in photonic crystals with topological phases that sup- port one-way light propagation channels resilient to engineering imperfections. Here, we uncover the symmetry principles that enable such reflectionless channels in suitably designed graphene- like photonic crystals. We consider a wide class of nonreciprocal perturbations of photonic graphene compatible with energy con- servation, including gyromagnetic, pseudo-Tellegen, and moving medium responses. These perturbations are described by scalar and vector fields, as they can exhibit arbitrary spatial variations. Using tight-binding models, we examine how the nonreciprocal fields influence the crystal’s topology. Our findings reveal that nonreciprocal interactions alone cannot induce a topologically nontrivial phase. Instead, a nontrivial p6m-symmetric component in the nonreciprocal fields is required to open a topological bulk bandgap supporting edge states immune to reflections.