Blue light is only emitted if the blue subpixel is lit (well, except for some backlight leakage on LCDs). So it is possible to sit in front of a screen without any blue light. Of course, this means you can't produce most colors, so it's not ideal for general use, but it is possible.

When in bed at night, I often use a software filter to cut out all but red subpixels. This allows me to read or work without causing melatonin suppression. Just clamping blue and green to 0 is a very poor solution though; I should swap to a proper "redscale" filter (think greyscale, but only red subpixels) that is based on the luminosity of the source image. The dumb filter has definitely confused me a few times when I can't seem to highlight any text.