Why do some Air Forces not allow Color Blind Pilots?
In fact, most militaries don't take colorblind people into flight school.

Colorblindness can be a serious problem for a pilot, because in the interest of cost and/or simplicity, not all indicators in an aircraft cockpit are colorblind-accessible. It's really cheap to use a two-way red/green LED as a status indicator (and by quickly alternating the current through the LED you get amber); it's much more expensive in electro-mechanical systems to combine text and color so that the status can be deciphered by someone who is red-green colorblind. It becomes easier again in a glass cockpit, but that increases cost and there are still concerns like screen resolution to consider when designing text-and-color displays. While it's in the general interest of aviation manufacturers to design certain avionics with as many overlapping visual cues as possible, it's not always feasible to specifically design towards colorblind accessibility in every circumstance.

Here is a set of spectra simulating how various forms of colorblindness would change a person's perception of the normal color set:



Protanopia and deuteranopia are various forms of red-green colorblindness, the most common form of dichromia (protanopia is a deficiency in red cells, deuteranopia a deficiency in green; the results are similar because red and green are close in wavelength). Tritanopia is commonly called blue-yellow colorblindness and is less common, with full colorblindness (monochromia) being very rare.

From this chart, we can deduce the following basic difficulties for a red-green colorblind person attempting to operate a plane:


Red on brown, or any dark color, would have no contrast. That would make reading (and setting) this Cessna radio stack nearly impossible:



... as well as decreasing the contrast of red lines on high-elevation sectionals (like Charlie/Echo space boundaries, non-towered airports, NDB frequencies etc):


Green and yellow are practically indistinguishable. That would make discerning the borders of inhabited low-lying areas on sectionals difficult:



... as well as making the color-coding of this airspeed gauge much less useful at a glance:


Blue and magenta are indistinguishable, as are cyan and white. That makes your GPS useless over water; where's the magenta line?




While you could probably get around most of these difficulties (buy a nav stack with blue LED displays, trace the borders of your sectional charts in something, configure the GPS to give you a white line, etc etc) these are all images that people with full color vision would be able to discern at a glance, which in an emergency situation is often a life-or-death advantage.

That point is especially true for military pilots, who are typically subject to more rigorous medical screening and training including very high requirements for visual acuity (often better than 20/20 uncorrected vision). If you can't see extremely well in a combat situation, you will either fail to spot an enemy until he has gained a significant advantage over you, or you will fire on friendly forces; either way, you're a liability. Coupled with the fact that everyone and their brother grew up dreaming of being a fighter pilot, flight schools get to be picky. Therefore, military aircraft cockpits are typically designed with the assumption of full color spectrum perception, because the only people who will ever be in them will be able to tell red from green, blue from yellow.

Consider, just as one example, a hypothetical conflict in the Middle East involving the Turks and Iranians, where NATO and thus the USAF is also involved. Both of these countries still operate variants of the F-4 Phantom. With an ROE requiring visual confirmation of a hostile, if you are in a USAF F-22, in a visual-range tangle with an F-4 whose IFF is inconclusive (either non-functioning or malfunctioning) and you can't tell the difference between these two rondels...



... you are screwed. The fact the Phantom is maneuvering against you is what any pilot would do when approached by an aggressor aircraft; a Turkish pilot isn't just going to sit there and be shot down by friendly fire, he'll engage defensive, so you can either shoot and risk spending the rest of your life in Leavenworth for dereliction of duty, or break engagement, presenting your tailpipe to the other craft and hoping it's not hostile. Fifty-fifty shot either way with a hundred and fifty million dollar plane on the line, not to mention your life. Your first clue it's an Iranian would be a missile launch, and no matter how much more advanced USAF craft are now than in the era of the F-4, an aircraft that has successfully launched a short-range missile at you has you by the wrinkly ones.

In addition, ground lighting systems are often not differentiable either. For instance, there is an important difference between a heliport beacon flashing green-yellow-white versus white-green-red (the one including a red flash is a hospital helipad and off-limits to gen-av traffic even in an emergency), but a red-green colorblind person may well not be able to tell the difference. Runway end lights are either green or red, indicating traffic direction (though there's usually a secondary cue of the approach array lights sequencing toward or away from the runway edge). Similarly, to a person for whom red is indistinguishable from white, the red-over-white glide slope indicator at the end of the runway would be useless (this would typically happen only with full colorblindness). Blue-yellow colorblindness is the other major type of partial colorblindness, and it would cause other problems like decreasing readability of navigation charts (for instance, incorporated land areas are yellow on FAA sectionals, while Victor routes and class B/D airspace borders are different blues) and trouble negotiating taxiways as the blue taxiway lights would look the same as yellow-white indicator lights elsewhere on the tarmac.