Why doesn't Clopyralid damage cool season lawn grasses?
Auxins are a class of phytohormones involved in plant growth and behavior. Auxinic herbicides, such as clopyralid, induce an overinduction of the auxin response in susceptible plants (kelly &amp; Riechers, 2007). From the Kelly &amp; Riechers 2007 article I quote:


  [Auxinic herbicides] cause various growth abnormalities in sensitive dicots, ranging from leaf epinasty and/or cupping and stem twisting, to thickening of stems and roots, and ultimately chlorosis and necrosis [...]. Lack of phytotoxicity in grasses has been attributed to several factors, including anatomical differences in vascular structure and differences in ability to metabolize the herbicide [...]


Hence, grasses seem to be protected due to anatomical and metabolic differences. Specifically, auxinic herbicides seem to kill dicots and spare monocots (Song, 2014). Song explains, and I quote:


  However, the underlying molecular mechanism of how auxinic herbicides selectively kill dicots and spare monocots is not understood yet [...]. Early research has
  proposed that the selectivity of auxinic herbicide is because of either limited translocation or rapid degradation of exogenous auxin, altered vascular anatomy, or altered perception of auxin in monocots [...] The difference in vascular tissue structure between dicots and monocots may contribute to the selectivity of auxinic herbicides. In monocot stems, the vascular tissues (the phloem and xylem) are scattered in bundles, and lack a vascular cambium; in dicot stems, the vascular tissues are formed in rings and possess a cambium. 


So in all, the exact mechanism of specificity between monocots and dicots is unclear, but may be related to structural and/or metabolical (pharmacokinetical) and/or different pharmacodynamical differences between monocots and dicots in general. Dicots are susceptible to auxin herbicides, while grasses, being monocots, are protected. 

The complexity of the auxin hormonal system (Song, 2014) may explain why differences exist between grass species, but this is speculative.     

References
Kelly &amp; Riechers, Pesticide Biochem Physiol 2007;89:1–11
Song, J Integr Plant Biol 2014; 56:106–13