Found with Fuji that you have to turn down the Sharpness of the files (I use -2), and that gets rid of the plasticky look you're seeing. Tradeoff is you have to add a little sharpening back in post if you want the best results. I only shoot jpg out of my Fujis, more often than not I transfer files to my iPhone for sharing, edit them using the iPhone, and I add exactly +14 sharpness... 15 is too much, 14 is perfect
Definitely see the green cast in my Nikon files (D500, Z9), especially since I use them to shoot birds in foliage. Easy fix in post w/ the tint slider.
Canon, on the other hand, has always had a red/magenta tint tendency. It used to be really bad back in the 5D2/3 days, where the camera would blow out the red channel if you weren't careful. With the R5, I don't see that as much, and the files are so awesome to work with.
Nowadays, the gap b/w Canon and Nikon is about zero, you can get amazing files out of both systems. All of the DR and AF advantages that Sony and Nikon had have been pretty much erased with the RF mount. More important things to base a system choice on now.
Of the three brands I shoot, Fuji is easily the most fun. The look you can achieve with it is sublimely beautiful (especially w/ the Fuji 35 f/1.4). At the same time though, having shot countless times alongside my wife's R5 + 24-70 f/2.8, the Canon files are a good notch better, they're so clear and lush; the Canon is ultimately the camera we choose if we're shooting for serious.
The thing is though... Canon used to have such an awesome lineup of lenses that possessed a more characterful, old school feel: the EF 50 f/1.2L, 135L, 35 f/1.4L, 85 f/1.2L II... they've completely abandoned any sense of character, instead choosing to compete w/ robot Sony in the pursuit of clinical perfection and winning test chart shooting awards (same with Nikon, they too have some legendary glass). That's why I devote my casual shooting to Fuji anymore, I am more than willing to give up boring clinical perfection, for more character and feel being imparted on my photos. Yeah, yeah, we can always adapt the classic glass, but it'd be nice to see them embrace some artful side of design in future product releases.
I still have not decided about dumping my Canon, been close a number of times and the one thing that has stopped me is the 135L I have. Paired with 5D3 the images are striking and the skin tones always perfect. I don't know about other peoples 5D3s but my images always have been just right skin tone wise. I've never seen a magenta hue at all or maybe I'm blind to it. I also own three other canon lenses so its hard to get rid of something that is not broken. I have an emotional attachment to the camera. With my Fuji, its more fun but getting the tones right on skin has taken me some work at times. Fuji is perfect for everything else, wildlife looks amazing, buildings look great, amazing colours for abstract. I may end up hanging onto the old canon yet, same as I hardly touch my old Fuji X100 but cant sell it. Am I abnormal or what? 
Their focus on higher end products may have reduced their market share for camera sales, but seems to have made them quite profitable:
