I can give you one good reason to answer the door, at least where I live. If you don't, you are setting yourself up for a burglary that will turn into a home invasion.
Here's how it works, and as a Police Officer, I am sure you know this.
They knock on your door. Usually it is during the day. If someone answers they come up with something lame. Like asking for directions or if you need work done around your home.
If no one answers, they slip around back, try the back door, try the windows, and if they find something open, your home gets burglarized.
Now, if you ARE home and don't answer the door, and the bad guy comes in, you have a highly volatile situation on your hands.
It's better, at least in my mind, to let them know in no uncertain terms that the anti gun neighbor is a much better target for them than my home is ever going to be.
Yes its a problem if they make it inside the home. And the state you live in makes a great deal of difference. Here is a
case that interested me that happened in Maryland.
A man's home is his castle, except in Maryland. Man shoots intruder at 2am, gets charged with murder - Bullets First | Bullets First
maryland-man-shoots-intruder-2am-gets-charged-murder/
In Texas this homeowner would never have been charged,
unless the shooting took place outside the homeowner's home.
But in Maryland the laws are different. In Texas if he were charged it would have been no billed by the grand jury.
For one thing everyone ought to have a secure door, so secure that it is clear beyond doubt that the intruder broke his way in.
If it is during the day, more folks are far more likely to open the
door than at night, so I suspect that those wanting to do a burglary most likely will check during the day time, to try and
see if a homeowner is home or not. If the would be intruder is
high on meth he is not likely to care whether you are home at
night, or daytime either one, but is only interested in stealing
something of value to support his habit. As for slipping around
back I am glad I have no back door, so there is only one avenue
for someone to come in with secure windows.