Microbial communities are found all across the biosphere, from human guts to glaciers, from soil to activated sludge. Understanding common properties of such diverse communities can pave the way to elucidate the common mechanisms behind their patterns of correlations, stability, and resilience. In particular, shedding light on how bacteria interact as a function of their genetic similarity is extremely relevant both at the fundamental and practical levels. Using data from natural communities and mathematical modelling, we discover  a macroecological law relating mean correlation with genetic similarity, revealing that correlation goes from positive to null values by increasing species dissimilarity. Fluctuations of shared environmental factors, such as temperature or resources, are responsible for such a universal pattern.