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.

I suspect this isn’t the case with an OLED, since it wouldn’t even emit any blue light in the first place if those pixels aren’t on. However, a typical laptop / monitor will have a white backlight that then gets blocked. Often there’s bleed through even if the screen is completely black.

If someone with more specific knowledge about screens corrects me, I yield to their judgment. :)

tech writer who specializes in TV screens here. You are indeed correct. With OLED, no bleed-through at all exists since there is no backlight and unless specific RGBW pixels on the screen are activated, they emit no light at all basically. On the other hand, even the absolute best consumer market LCD/LED screens leak at least some backlight glow, though in high quality models it becomes very faint due to local dimming zones and high quality light blocking.