Not arguing that police should have qualified immunity (which seems to be the big point you're making if I'm understanding it correctly), but are you saying that there are no differences between police and ordinary civilians?
If so, would you say that police have no more responsibility to protect other citizens than an ordinary citizen would have? If so, does that mean that I as an ordinary citizen have just as much responsibility to protect others as they do - meaning I should go around carrying a gun at most/all times (if you feel the police should), chase down and apprehend people who rob stores if I see it, etc.
Lots of professionals have lots of obligations to do lots of things. We still call them civilians.
Also, there is no federal law that say that an on-duty police officer must stop an armed robbery. The level of discretion that we give to police is greater than many other professions.
If you go by the dictionary definition, they are not civilians, as police are excluded (as are firefighters in certain definitions). I'm not really worried, though, about what word you choose to use or how you choose to define civilians.
I am curious as to what your thought are about differences, if any, between police and the general public, let's say. Do you see no difference at all? I am aware that federal law has been decided that on-duty police do not have a legal obligation to stop crime while, as you say, they are simultaneously granted qualified immunity. It does seem a bit like the best of both worlds from that perspective.
That being said, I'm curious if you feel they should have a responsibility beyond common citizens to protect others. If so, should that lend them any special treatment at all in your eyes such as GuitarStv's benefit of the doubt example?