I think it would depend on the particular mapping from 3 to 2 dimensions... it might be possible.
It surely depends on the type of colorblindness, there are many .
If you're monochromate or dichromate, I doubt that this is possible. Monochromates or dichromates are simply missing one or two color components out of three.
If you have anomalous trichromacy, you can by creating a monitor with pixels of different colors.
In any case, I don't see how it is possible to identify a tetrachromate with a trichromate (RGB) monitor.
I tried to increase the contrast and change the hue of the color test to understand what was different between the apparently similar colors but I wasn't able to find any difference.