Kin discrimination describes the differential interaction of organisms with kin versus non-kin. In microorganisms, many genetic loci act as effective kin-discrimination systems, such as kin-directed help and non-kin-directed harm. Another important example is facultative cooperation, where cooperators increase their investment in group-directed cooperation with the abundance of their kin in the group. Many of these kin-discrimination loci are highly diversified, yet it remains unclear what evolutionary mechanisms maintain this diversity, and how it is affected by population structure. Here, we demonstrate the unique dependence of kin-discriminative interactions on population structure, and how this could explain facultative-cooperation allele-diversity. We show mathematically that low relatedness between microbes in non-clonal social groups is needed to maintain the diversity of facultative-cooperation alleles, while high clonality is needed to stabilize this diversity against cheating. Interestingly, we demonstrate with simulations that such population structure occurs naturally in expanding microbial colonies. Finally, analysis of experimental data of quorum-sensing mediated facultative cooperation, in Bacillus subtilis, demonstrates the relevance of our results to realistic microbial interactions, due to their intrinsic non-linear frequency dependence. Our analysis therefore stresses the impact of clonality on the interplay between exploitation and kin discrimination and portrays a way for the evolution of facultative cooperation.