Prions are self-propagating alternative states of protein domains. They are linked to both diseases and functional protein roles in eukaryotes. Prion-forming domains in Saccharomyces cerevisiae are typically domains with high intrinsic protein disorder (i.e., that remain unfolded in the cell during at least some part of their functioning), that are converted to self-replicating amyloid forms. S. cerevisiae is a member of the fungal class Saccharomycetes, during the evolution of which a large population of prion-like domains has appeared. It is still unclear what principles might govern the molecular evolution of prion-forming domains, and intrinsically disordered domains generally. Here, it is discovered that in a set of such prion-forming domains some evolve in the fungal class Saccharomycetes in such a way as to absorb general mutation biases across millions of years, whereas others do not, indicating a spectrum of selection pressures on composition and sequence. Thus, if the bias-absorbing prion formers are conserving a prion-forming capability, then this capability is not interfered with by the absorption of bias changes over the duration of evolutionary epochs. Evidence is discovered for selective constraint against the occurrence of lysine residues (which likely disrupt prion formation) in S. cerevisiae prion-forming domains as they evolve across Saccharomycetes. These results provide a case study of the absorption of mutational trends by compositionally biased domains, and suggest methodology for assessing selection pressures on the composition of intrinsically disordered regions.