You can try to find loop holes in the law that allow you to do certain things, but it will not always be possible. Bottom line, there WILL be times when you will need to do something forbidden when there are no exceptions allowing it. You have to ask yourself, if you were in this situation, would you refuse to do whatever it was? If so, then the military is definitely not for you. As others have stated, you can try to plan for how to face these issues, but in many cases things that may seem reasonable to you now will not be possible. Things like the security camera thing or the unplugged laptop. For example, if you become an intel officer, you will work in a secure, locked room (possibly with only yourself and a female). Since it is a classified environment, there are no cameras allowed, and you cannot use your own laptop because you will need to access secret information on a government computer. So you see, it is not just the flying world where you could run into problems.
If you are asked to do something incompatible with your beliefs and there is a loophole or exception that allows it, great. You can do your job and reconcile it with your faith. But if there is not an exception that allows whatever it is, you WILL still have to do it. That's just the honest truth. If you can make peace with the fact that there will be times when you will have to make exceptions to your lifestyle knowing that you tried your best, then you can probably make it work. If being forced to operate electronics on certain days, be alone with females, eat non-kosher food etc is going to eat you up inside, then you should pursue a different profession.