Most species distributions are dynamic, and as species distributions change they often encounter novel environments and resident species. To establish new populations, ecologically similar species compete with residents for resources while adapting to the environment. Yet local adaptation in residents can allow them to outcompete maladapted invaders and prevent their establishment. Indeed, local adaptation often improves male condition but also intensifies sexual conflict, a process where males increase their fitness while decreasing female fitness. Using an eco-evolutionary model, we show that sexual conflict can prevent adapted residents from monopolizing resources. This cost of adaptation in the residents opens a window of opportunity for the establishment of maladapted invaders. Female resistance to male harm can, however, prevent the invader from establishing. Sexual conflict can therefore reduce differences in competitive ability, facilitating establishment, but does not affect niche differences. However, when sexual conflict is density dependent, it can facilitate resident and invader coexistence, even when interspecific competition is stronger than intraspecific competition. Our results show that reproductive interactions may critically shape the dynamics of species invasions and species coexistence.