Selfish genetic elements (SGEs) that spread by manipulating spermatogenesis often have highly deleterious effects on males that carry them. Females that mate with male carriers of SGEs can also suffer significant costs: they receive fewer and poorer-quality sperm, their offspring will inherit the deleterious allele, and the sex ratio of their offspring will be biased towards the more common sex. To counter these costs, females are therefore expected to prefer to mate with males that do not carry sex ratio distorters or other deleterious selfish genetic elements. However, despite the potential costs, there are few examples of female choice against males carrying SGEs. We searched for evidence of a female preference in fruit fly Drosophila pseudoobscura against males carrying a costly meiotic driving X-chromosome Sex Ratio (SR). In a series of five non-competitive mate preference experiments, we find no evidence that females prefer to mate with non-SR males. Our use of five separate experiments, involving more than 800 females, makes it unlikely that this lack of a difference was due to low power or simple chance. We suggest that the lack of female choice against SGE-carrying males may be due to strong selection on SGEs to be indistinguishable from alternative alleles. Furthermore, polyandry, either in direct response to receiving an ejaculate from an SGE-carrying male or carried out indiscriminately when at risk of mating with carriers, may be an alternative response by females to limit the exposure of their offspring to SGEs.