I think the problem is that LUT’s have only recently started becoming more common in still photography, even though they’ve been relatively common in a video workflow for a while. I can understand the frustration.
Another part of the problem is that color (and colorspaces) is not as simple as many folks would believe. It’s a complex subject that starts to get more complex the further you go from more common color spaces like sRGB and AdobeRGB (hence the questions from @ilias_giarimis).
If you want a simple solution, we just need to get your CineStyle LUTs into a format that RawTherapee can use directly (HaldCLUT). Would it be possible for you to upload the files somewhere for us to investigate them? If so, someone might be able to generate a HaldCLUT version for you to use directly with your images.
If you happen to have a file that you don’t mind publicly sharing with us to use as a reference, we can collaborate to get you what you need! 
[edit] - just found this: