The effects of protein surface potential on the self-assembly of protein polymer block copolymers are investigated in globular proteins with controlled shape through two approaches: comparison of self-assembly of mCherry-poly(N-isopropylacrylamide) (PNIPAM) bioconjugates with structurally homologous enhanced green fluorescent protein (EGFP)-PNIPAM bioconjugates, and mutants of mCherry with altered electrostatic patchiness. Despite large changes in amino acid sequence, the temperature-concentration phase diagrams of EGFP-PNIPAM and mCherry-PNIPAM conjugates have similar phase transition concentrations. Both materials form identical phases at two different coil fractions below the PNIPAM thermal transition temperature and in the bulk. However, at temperatures above the thermoresponsive transition, mCherry conjugates form hexagonal phases at high concentrations while EGFP conjugates form a disordered micellar phase. At lower concentration, mCherry shows a two-phase region while EGFP forms homogeneous disordered micellar structures, reflecting the effect of changes in micellar stability. Conjugates of four mCherry variants with changes to their electrostatic surface patchiness also showed minimal change in phase behavior, suggesting that surface patchiness has only a small effect on the self-assembly process. Measurements of protein/polymer miscibility, second virial coefficients, and zeta potential show that these coarse-grained interactions are similar between mCherry and EGFP, indicating that coarse-grained interactions largely capture the relevant physics for soluble, monomeric globular protein polymer conjugate self-assembly.