Relationship of RNA-binding proteins to peptidyl-prolyl cis-trans isomerase
Without seeing the sequence of the RNA-binding protein it is impossible to be sure, but the obvious conclusion is: 


  The RNA-binding protein is a peptidyl-prolyl cis-trans isomerase.


It has been known since 1989 that peptidyl-prolyl cis-trans isomerase is a multiple-function protein, also exhibiting properties of the cyclophilins, proteins which bind cyclosporin A. The post raised the possibility that it may have other activities and a literature search reveals several more recent papers that indicate cylcophilin A can bind certain RNAs. I list some of the titles:

A nuclear RNA-binding cyclophilin in human T cells (1996) FEBS Letters 398 201–205

Molecular cloning, structure and expression of a novel nuclear RNA-binding cyclophilin-like gene (PPIL4) from human fetal brain (2001) Cytogenet Cell Genet 95 43–47

Cyclophilin A Binds to the Viral RNA and Replication Proteins, Resulting in Inhibition of Tombusviral Replicase Assembly (2013) J. Virol. 87 13330–13342

Structure of RNA-interacting Cyclophilin A-like protein from Piriformospora indica that provides salinity-stress tolerance in plants (2013) Scientific Reports 3 : 3001, DOI: 10.1038/srep03001