Intra-locus sexual conflict, or sexual antagonism, occurs when alleles have opposing fitness effects in the two sexes. Previous theory suggests that sexual antagonism is a driver of genetic variation by generating balancing selection. However, these studies assume that populations are well-mixed, neglecting the effects of spatial subdivision. Here we use mathematical modelling to show that limited dispersal can fundamentally change evolution at sexually antagonistic autosomal and X-linked loci due to inbreeding and sex-specific kin competition. We find that if the sexes disperse at different rates, kin competition within the philopatric sex biases intralocus conflict in favour of the more dispersive sex. Furthermore, kin competition diminishes the strength of balancing selection relative to genetic drift, reducing genetic variation in small subdivided populations. Meanwhile, by decreasing heterozygosity, inbreeding reduces the scope for sexually antagonistic polymorphism due to non-additive allelic effects, and this occurs to a greater extent on the X-chromosome than autosomes. Overall, our results demonstrate that spatial structure is an important factor in predicting where to expect sexually antagonistic alleles. We suggest that observed interspecific and intragenomic variation in sexual antagonism may be explained by sex-specific dispersal ecology and demography.