I am not seeing any change, except in the histogram, when I turn the CR-filter-component eye on and off.
In more detail:
I have an sRGB-sized gamut monitor but use a ProPhotoRGB workspace in PS. I copy-pasted a crop of your left, more saturated screenshot into PS and assigned it an sRGB profile. Your PNG screenshot didn't contain any color profile so I just guessed it was sRGB. Your monitor could be wide-gamut in which case I should have assigned AdobeRGB to be approximately correct. Because my monitor is approximately sRGB and the image was assigned a profile of sRGB, despite the workspace being a larger ProPhotoRGB, no pixels are outside the monitor gamut, because both the image and the monitor are sRGB.
On the image I'd just pasted into a new PS document, I created a smart object then added the CR-filter and clicked Ok without changing anything and I don't see any desaturation or other visual difference when I turn the smart-filter CR eye on and off; however, I do see the histogram change. CR uses an internal ProPhotoRGB-wide colorspace and I think this is why I see the histogram change so much when I turned the CR-filter component eye on and off--PS is showing me the histogram as if the image is in ProPhotoRGB instead of sRGB.
I then converted the sRGB image to ProPhotoRGB, and repeated the same SO-CR-filter, eye-on-off, and the online version still doesn't change, but this time the histogram doesn't, much, eitehr, because the image colorspace and the CR-workingspace are similar.
Since your image is changing, I'm suspicious that there are some CR sliders set to non-zero, somewhere, or your monitor profile is very out-of-whack, so PS isn't actually displaying the proper colors.
The desaturation is about what would be expected if you were viewing an AdobeRGB image using an sRGB profile. Without knowing what monitor you have and whether your monitor profile is properly created, it's hard to guess what is wrong for you.
If you want to upload your PSD, to maybe www.dropbox.com, and post a public download link to it, here, someone might be able to test what happens for them. I don't have a ColorEfex filter on my side so I'm not sure if that would affect things. Uploading a version of the image without the ColorEfex smart filter might be good.