Okay, my two cents after reading all of the above.
1. Military personnel in uniform: Regs are pretty specific and clear...leather jackets are to be worn by aviation designated personnel only. Pilots, NFOs, Flight surgeons, aircrew, aviation physiologists, etc. Got wings (the only exception being Aviation Supply Officers or Navy Parachutist qualified personnel...NOT aviation designations...but a qualification badges...)? Wear the leather jacket. I believe that also applies to "prior designated aviation personnel who are still authorized to wear the warfare device"...guys who went to law school and became JAGs, etc. But...didn't get your wings or had them pulled, or (more rarely) turned them in? Then hang the jacket lovingly in your closet and don't wear it in uniform. Not authorized anymore.
2. Nylon jackets are more problematical...can be issued to anyone as organizational clothing, but when I last paid attention (2002), they really weren't authorized with anything but flight clothing or a working uniform "in the spaces/flightline/ship", etc. Not appropriate for "out in town", any more than those working uniforms were.
3. Simply no rules apply to the civilian community. You would think a certain amount of "good sense" would apply to DoD/Navy civilian employees in the workplace, but I sorta agree with the "don't go there" comments above...unless the jackets are being worn in some way to discredit Naval aviation, which I gather is not the case.
4. As a former battlegroup Chief of Staff, for a number of SWO flag officers, it was always my duty (gulp) to politely inform the "new boss" that even though CAG gave him a leather flight jacket, he was not authorized to wear it. They were usually thankful for the vector that would keep them from setting a poor example and potentially embarrasing themselves. I always smiled that I spent "most days underway" in my blue coveralls, while my SWO bosses spent the time in their new flight suits. Past the last sea bouy, who cared?
5. "Enforcement" of the above is a leadership issue. I, as a VF squadron CO, would have been the guy to politely tell my AI that he was out of uniform...I wouldn't leave it up to his JO peers to square him away, although they would be correct to do so.
In my second career, I have developed an affinity for wearing a very nice USAF-style A2 leather jacket as a casual alternative to a suit or sport coat. So far no USAF guys have braced be up in the airport...but I don't wear any patches or nametags.
Yours in sartorial excellence, Spike