Hybridization is an important source of variation; it transfers adaptive genetic variation across species boundaries and generates new species. Yet, the limits to viable hybrid genome formation are poorly understood. Here we investigated to what extent hybrid genomes are free to evolve by sequencing the genomes of four island populations of the homoploid hybrid Italian sparrow Passer italiae. We report that a variety of novel and fully functional hybrid genomic combinations are likely to have arisen independently on Crete, Corsica, Sicily and Malta, with differentiation in candidate genes for beak shape and plumage colour. However, certain genomic regions are invariably inherited from the same parent species, limiting variation. These regions are over-represented on the Z chromosome and harbour candidate incompatibility loci, including DNA-repair and mitonuclear genes. These gene classes may contribute to the general reduction of introgression on sex chromosomes. This study demonstrates that hybrid genomes may vary, and identifies new candidate reproductive isolation genes.