In many populations, unequal numbers of females and males reproduce each generation. This imbalance in the breeding sex ratio (BSR) shapes patterns of genetic variation on the sex chromosomes and the autosomes in distinct ways. Despite recognition of this phenomenon, effects of the BSR on some aspects of variation remain unclear, especially for populations with non-equilibrium demographic histories. To address this gap in the field, we used coalescent simulations to examine relative patterns of variation at X-linked loci and autosomal loci in populations spanning the range of BSR with historical changes in population size. Shifts in BSR away from 1:1 reduce nucleotide diversity and the number of unique haplotypes and increase linkage disequilibrium and the frequency of the most common haplotype, with contrasting effects on X-linked loci and autosomal loci. Strong population bottlenecks transform relationships between the BSR, the site frequency spectrum, and linkage disequilibrium while relationships between the BSR, nucleotide diversity, and haplotype characteristics are broadly conserved. Our findings indicate that evolutionary interpretations of variation on the X chromosome should consider the combined effects of the BSR and demographic history. The genomic signatures we report could be used to reconstruct these fundamental population parameters from genomic data in natural populations.