I can understand some of what you're trying to bring across but then you posted the above.
I think we're off topic now but, in respect to the bold type, what the heck are you talking about? The example given doesn't even exist, thereby rendering your answer without merit. The other conclusion I've drawn based on that "example" is that you are unfamiliar as to what rules, restrictions, and laws the individual soldier abides by in official vs unofficial capacities.
If it's allowed, I'd like to see you give a better explanation, with a real example this time, of what these special rights are that soldiers receive.
In the US, federal law (somewhere in 18 USC 1716) restricts the sale of many folding knives designed to be operated with one hand, commonly referred to as "automatic" knives, to a short list of people including active duty military personnel. So a navy radar tech can buy a Benchmade 5000 per federal law, a civilian doing the same job cannot. Many states mirror the federal laws, so even though the code I cited is federal, there are equivalent restrictions at the state or even local level, most of which have the same carve-outs. The result is that when I am in those states I cannot buy or carry something an active duty army cook can.
Some states allow such knives to everyone. Even then, the federal restrictions impinge. I happen to have a Benchmade auto knife, which is legal for me to carry in Texas. I do not get the Benchmade warranty, however, because I am unable to ship my knife to Oregon for service.
I'm also trying to understand where the tie-in exists between your above post and LEOs carrying on/off duty in businesses.
Consider it this way: It is possible to write the laws so that LEOs can carry on the job, and off the job, without making them a special class of people. You simply write the carry laws in such a way that they can apply to everyone. This is true for most police powers actually. It is not necessary to grant police special powers to arrest, for example. E.g. in California (and many other places) I can arrest someone just as a LEO does. Of course if I am wrong about it I am exposed to mucho liability that an officer in the course of her duties is not personally exposed to (though her department/city is), but the power is the same.
Where things get ugly, however, is when people want to impose restrictions. Carry restrictions are quite old so it is harder for most people to relate to them, but magazine capacity is a good current example. The argument is the same for both.
When a politician wants to restrict sales of magazines of over 10rd capacity, some of the first groups to state an objection for themselves are police unions. Police officers, they argue, cannot operate under that restriction. And that's fine, I don't think anyone should. The problem is that instead of accepting that the police use case invalidates the restriction, they then carve out an exemption for police.
Same with carry laws. When faced with CCW reciprocity issues, rather than saying, "this is evidence we need national Concealed Carry reciprocity," they carved out a rule for a small portion of the population. When faced with the reality that carry restrictions (open or concealed) would prevent off duty police officers from carrying, which is evidence that the carry restriction is broken, they carved out a LEO exemption rather than fixing the problem for everyone.
That isn't an accident or oversight of course. It is collusion. It is an organized effort between the politicians and the special interests (police unions in this case) to restrict most citizens from exercising the same 2A rights that LEOs are exercising when they carry (whether they think of it that way or not). It isn't unreasonable to call the restriction of rights people need in their day to day lives to be opression.
Which is where the social aspect comes in. By going along with an agreement to restrict the rights of most citizens as long as they could continue to exercise theirs, police officers got drawn into a battle and put themselves on the wrong side as far as most citizens who notice will be concerned. That isn't going to lead to positive feelings. It is downright divisive in fact. It will color perceptions and lead to unfriendly interactions, which is a vicious downward spiral cops shouldn't want to be caught up in.
An off duty cop should have the same right to carry as any other citizen. No more, no less. Anything else is harmful to everyone including the cops.