For solid-solution Ba1−xKxFe2As2 Fermi surface evolution is mapped via Bloch spectral functions calculated using density functional theory implemented in Korringa-Kohn-Rostoker multiple scattering theory with the coherent-potential approximation. Spectral functions reveal electronic dispersion, topology, orbital character, and broadening (electron-lifetime effects) due to chemical disorder. Dissolution of electron cylinders occurs near x∼0.9 with a nonuniform, topological (Lifshitz) transition, reducing the interband interactions; yet the dispersion maintains its dxz or dyz character. Formation energies indicate alloying at x=0.35, as observed, and a tendency for segregation on the K-rich (x>0.6) side, explaining the difficulty of controlling sample quality and the conflicting results between characterized electronic structures. Our results reveal Fermi surface transitions in alloyed samples that influence s± to nodal superconductivity and suggest the origin for deviations of common trends in Fe-based superconductors, such as Bud’ko-Ni-Canfield scaling.