The 3D LUTs from PRO EDU will work with any camera's files; however, those working with Fuji files in Capture One will need to use a different setting to see the impact of the colors on their images.
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3D LUTs are similar to presets or color actions, except they are introduced as the first step in post-processing during the raw phase of image correction. 3D LUTs are inserted into the raw image in an adjustable format giving users the ability to infuse color prior to starting the normal post-processing workflow. Users can read more about the 3D LUTs here: What Versions Of Lightroom And Camera RAW Will The 3D LUTS Work With?

Fuji users have reported some issues with using 3D Luts in Capture One.

PRO EDU testers have found with the Fuji RAW files that the 3D LUT files ONLY work when the "Curve" in the "Base Characteristics" section is set to "Film Extra Shadow", "Film High Contrast", "Film Standard", or "Linear Response". They do not work in any "Fujifilm" simulated film Curve, or in "Auto".