Why can acidification of solution lead to selective precipitation of ions such as Fe2+ and Zn2+?
FeS has 1500 times the solubility of ZnS.  Given the slow addition of a small molar fraction of acid that solubilizes both Zn(II) and Fe(II), that fraction will retain at equilibrium.  It gets complicated if soluble polysufides exist. Iron gives pyrite and marcasite ($\ce{FeS2}$) via mackinawite ($\ce{FeS}$) and greigite ($\ce{Fe3S4}$), but they are insoluble.