I am currently using a dual monitor which is MacBook Pro and an external Asus monitor.
The issue is not about RGB and CMYK. I also believe color profile couldn't help since this will also change my MacBook color as well.
The problem occurs when I drag the illustrator screen from MacBook to Asus screen, the color change from correct to a dull color. It doesn't affect the export images nor output file. It just looks so dull when I am working which is very frustrating. I have to drag it back to my MacBook screen to check the colors every time.
That's just because the ASUS Screen is trash 😉
Try to handle colors with your System Preferences – Colors/Screen.
I know it's not a good monitor for a designer. But I am sure it's not completely about the quality, as I mentioned the problem occurs only if I use adobe illustrator and photoshop. The color looks quite normal if I use "preview" or adobe PDF.
I think you are one of the many people who encounter this.
Is your external monitor connected through HDMI to HDMI, USB-C Thunderbolt to DisplayPort ?
If it is through HDMI, your M1 and Asus monitor most certainly negotiated YPbPr / YCbCr / YUV (colour space) mode instead of RGB (coulur space) mode. And USB-C Thunderbolt to DisplayPort is nowhere near a guarantee for RGB mode between M1 Macs and external monitors. This is a long standing Mac to external monitor issue (but not all external monitors). Intel based Macs can force RGB mode on the connection to the external monitor by overwriting the EDID data. But M1 based Macs cannot.
Here is just one of the many many discussions and attempted fixes : M1 Mac External Display - Fuzzy Fonts & Colors - YPBPR vs RGB . The Apple Community, Reddit, etc are littered with similar discussions and attempted fixes.
Eizo has a webpage dedicated to this : Apple M1 Chip Equipped Mac Computer and Monitor Compatibility . According to them all issues can be resolved with system/OS updates, except the "(1) Number of Monitors Supported" issue.
Check your external monitor's Input Colour Format for clues, and your M1 Mac's "System Information >> Hardware >> Graphics/Displays", and then on the right under "Displays:" also for clues.
If you use an Intel based Mac, here is one of the many scripts to fix this in EDID : A script to fix EDID problems on external monitors in macOS and also this thread : Help with EDID fix to Force RGB mode
If your Mac and external monitor did negotiate RGB (colour space) mode, you can try this : Change your Mac display’s color profile
Jeez! Why can't we edit posts? Just look how many additional posts I had to make to add some information.
It's out of my system now.