CRISPR-Cas immune systems are present in around half of bacterial genomes. Given the specificity and adaptability of this immune mechanism, it is perhaps surprising that they are not more widespread. Recent insights into the requirement for specific host factors for the function of some CRISPR-Cas subtypes, as well as the negative epistasis between CRISPR-Cas and other host genes, have shed light on potential reasons for the partial distribution of this immune strategy in bacteria. In this study, we examined how mutations in the bacterial mismatch repair system, which are frequently observed in natural and clinical isolates and cause elevated host mutation rates, influence the evolution of CRISPR-Cas–mediated immunity. We found that hosts with a high mutation rate very rarely evolved CRISPR-based immunity to phage compared to wild-type hosts. We explored the reason for this effect and found that the higher frequency at which surface mutants pre-exist in the mutator host background causes them to rapidly become the dominant phenotype under phage infection. These findings suggest that natural variation in bacterial mutation rates may, therefore, influence the distribution of CRISPR-Cas adaptive immune systems.