The MNase used for CUT&RUN also accepts RNA as substrate so it might be possible to adapt the CUT&RUN protocol for use on RNA binding proteins. RNA in the cytoplasm will attract the degradation machinery if it is lacking the 5' cap and the 3' poly-A tail. Therefore, I would suggest to use work with isolated nuclei. This has the additional benefit, that you can omit the digitonin in the buffers, which is used to replace the cholesterol and permeabilize the cell membrane. The isolated nuclei may then be immobilized using magnetic ConA beads like for a CUT&RUN experiment. An antibody against the protein of interest is added and subsequently the pAG-MNase is tethered to the antibody, thus bringing the MNase into proximity of the RNA of interest. Isolated RNA can then be reverse transcribed into cDNA to produce your sequencing library. In order to dispose of any contaminating DNA include a DNase treatment in the protocol subsequently to the RNA-prep and before the library prep. Normalization based on the E. coli DNA carried over with the MNase or a spike-in DNA is not an option in this case. Instead, consider using the total read numbers to normalize across samples or include a reference RNA of a known concentration.