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On page 165 of Star Wars Costumes The Original Trilogy it says "Beneath the flowing candy apple red robes of the Emperor's royal guard were matching red shirt, pants, leather gloves, and suede boots."

Here is a picture of the picture in the book it is referring to. I am only posting this because it's different from the ROTJ CRL.
https://i.imgur.com/7S5xPzJ.jpg

So I'm looking into getting my first ROTHJ RG outfit and I'm going off the CRL so I know it's done right but is this something that wouldn't be approved since it's not CRL or is this something that would be acceptable due to the source?

I have the costuming book too but I can only advise you to stick to the CRL only. This is all that the GMLs will refer to for approval. They won't be referring to any books. The official CRLs are on this forum to refer to.