On the contrary, when someone goes through security or gets a government ID I think its ok for us to tell them what to do. Regardless if it's against their culture to wear something or not. Religion should not trump security in any environment.
Now back to the topic and the picture. The only issue I have with her wearing it in the cockpit is the fact that she has her earphones over her hajib and maybe the loss of peripheral vision. I'd think she'd probably hear better with it underneath her hajib. But I'm gonna assume the wearing of the hajib is trumping the concern for muffled/unheard radio calls or the effect on her peripheral vision.
Your first paragraph is somewhat of a non sequitor, but I'll bite. For one, if that's what you think, then you need to really examine within yourself and determine whether you'd like it if someone told you what you could and could not wear or do because of security issues. If I were the TSA, I'd have everybody come onto the plane naked. That way they couldn't possibly hide anything of any kind in their garments. If that were the policy though, you can bet that people who value our culture-which says to be modest you have to wear
some clothing, and that clothing has to cover both your genitals and your upper torso-would be up in arms. The issuance of government ID, or the requirement to submit to a security screening, thankfully, in this country doesn't require that you dress in a particular way. However, we seem to think that we can require it of Muslims, and various other peoples because of our xenophobic fear of a culture that is drastically different than, and in many ways at odds with, our own.
To put this in perspective, I've worn longsleeve shirts and pants, as well as big jackets and hats through the security screening checkpoints. I've worn parkas through security. I have every right to (it was friggin' cold too). Why should a woman be forced remove her headscarf at these points when an American man wearing a ball cap (me), or a skull cap be allowed through without any harassment? So to say that somehow a hijab is somehow a threat to security, especially when if any additional screening is required, the woman may have a private screening with another woman is illogical.
Now, let's address your other paragraph. I've flown in airplanes that were loud and worn earplugs underneath my headset to protect my hearing, and the only reason I ever missed a radio call was inattention (read fatigue) or preoccupation (read task saturation). A rayon headscarf of sub-millimeter thickness isn't going to block out enough sound to be a safety hazard. And god forbid that anyone on this forum has ever listened to music in flight! THE HORROR!
Second, the issue of peripheral vision. This may be a valid point, however, I don't think its a particularly compelling one. Could there potentially be some sort of reduction in peripheral vision because of the way the scarf was wrapped? Sure, but I doubt it, have you ever even seen someone who wore a headscarf? Its not a burkha, their eyes are completely uncovered. I think the burden of proof would be on you on this one. If you come back with a legitimate, and entirely non-anecdotal study saying that the hijab causes reductions in peripheral vision that are unsafe for flying I'll change my tune.
However, speaking of anecdotes, when I was flying up north, I wore many large jackets. And on one day in particular, the heater (which didn't work too well anyway) broke about half way back from my destination. The airplane's door seals leaked like a sieve, s for that .4 on the way back, I had my hoody up over my head and synched down tight and a large polar jacket over that. On top of it all, a beanie. I noticed no reduction in peripheral vision.