We are getting what I consider dramatic differences in exports in Premiere Pro between the Program Monitor and the output. The outputs yes are compressed (H.264) but the significant drop in saturation is of concern. We can't relay on our program monitor anymore if the exports are so different. I have my own theories but I'd like to hear from the community first.
Mac Pro 2019
Footage is BlackMagic MOV exported to MP4 (H.264)
Hardware Encoding has been toggled on and off (two bottom images one on, one off)
Exported via Premiere (not media encoder)
Yes, it's a common issue that Adobe qualifies as being due to the fact that Premiere is set for broadcast gamma standards. Basically, higher contrast Gamma 2.4. I believe most web browsers, and perhaps even FCPX and QuickTime, playback video at Gamma 1.96, which is less contrasty.
I was referred to this free LUT you can download. After you do all your color grading in Premiere, apply this LUT as your last step. You will see this will alter your image, but after you export, you should get a result close to what you had before applying this LUT.