The development of reproductive barriers against parent species is crucial during hybrid speciation, and post-zygotic isolation can be important in this process. Genetic incompatibilities that normally isolate the parent species can become sorted in hybrids to form reproductive barriers towards either parent. However, the extent to which this sorting process is systematically biased and therefore predictable in which loci are involved and which alleles are favored is largely unknown. Theoretically, reduced fitness in hybrids due to the mixing of differentiated genomes can be resolved through rapid evolution towards allelic combinations ancestral to lineage-splitting of the parent species, as these alleles have successfully coexisted in the past. However, for each locus this effect may be influenced by its chromosomal location, function, and interactions with other loci. We use the Italian sparrow, a homoploid hybrid species that has developed post-zygotic barriers against its parent species, to investigate this prediction. We show significant bias towards fixation of the ancestral allele among 57 nuclear intragenic SNPs, particularly those with a mitochondrial function whose ancestral allele came from the same parent species as the mitochondria. Consistent with increased pleiotropy leading to stronger fitness effects, genes with more protein-protein interactions were more biased in favor of the ancestral allele. Furthermore, the number of protein-protein interactions was especially low among candidate incompatibilities still segregating within Italian sparrows, suggesting that low pleiotropy allows steep intraspecific clines in allele frequencies to form. Finally, we report evidence for pervasive epistatic interactions within one Italian sparrow population, particularly involving loci isolating the two parent species but not hybrid and parent. However there was a lack of classic incompatibilities and no admixture linkage disequilibrium. This suggests that parental genome admixture can continue to constrain evolution and prevent genome stabilization long after incompatibilities have been purged.