I have been unable to find a list of cameras that have false color on their internal monitor, so I'm starting to compile that list myself. I would rather not purchase a camera that didn't have false color.

Blackmagic
I have found false color to be indepsensible on my Blackmagic 6k G2 camera. Once I tried it, I assigned it to a hot key and I use it constantly. But, I am leaving Blackmagic design's cameras off this list as they pretty much all have false color. So just goto here and pick anyone you want.

Sony
The various Sony cinema line cameras (fx6, fx3, fx30) can support false color through a firmware update in their app or also via a LUT. I personally haven't tested out how user friendly that is but these cameras do not actually have native false color support in their internal monitors, so as of now, they do not make the list.

Cameras with False Color Support in their Internal Monitor

[1] Cannon R6 Mark II

[2] Cannon R5 Mark II

[2] Cannon C70