This would be simple to calculate using data downloaded from the D2P2 database (http://d2p2.pro/). I am not sure if systematic studies of this have been done before, but if they have they are likely to be on a small scale (perhaps by Dunker, using DisProt) or using a single predictor of disorder, e.g. in the methods papers of IUPred, PONDR, PrDOS, PV2, Dispred, etc. There is a paper by Rost which attempts to look at mutability (Schaefer et al. Bioinformatics 2010) but this is not quite what you ask.

Perhaps you should just do it!

I have a more specific suggestion than Julian. GPCR intracellular regions have many such unstructured domains and I am not sure how they vary among different animal phyla. This could be something you can think of, now that many GPCR structures are known, but not much about these flexible regions as density is usually missing in crystal structures. I am an interested party in the answers.

Hi De,

Giving you a different view than Julian and Sujay.

Unstructured or disordered regions are expected to show higher variability than structured regions in proteins. There have been few studies which might interest you.

(ex: Brown et. al., Mol Biol Evol 27(3): 609–621, 2010, Brown et al.,  2002). 

We did compare synonymous and non-synonymous mutation rates (dN/dS) in ordered and disordered human proteins and found higher dN/dS rates in disordered regions than in ordered regions of proteins. Amino acids of ordered regions contribute to secondary or tertiary structure of protein which is essential for its viability and hence many mutations are not retained. In case of disordered regions this does not hold good. Disordered regions in proteins are of 3 types : Conserved disorder, flexible disorder, non-conserved disorder (Bellay et al., 2010, genome biology). Conserved disorder is of interest as it harbors short linear motifs  (conserved sequence patterns). 

Hope this answers your question.