I don't understand why most of the discussion here is focused on what the woman was doing that night and how strange her behavior is, how intoxicated she was, or what laws she broke. The way I see it, the only really relevant question here is this - did he or did he not open the door? Because if he did I don't see how his actions are really justifiably. And her opening the door seems like the far less likely scenario here - if the door was unlocked she'd already be in the house when she was shot. But the door was probably not unlocked to begin with.
You can't say he acted out of survival instinct to protect himself or even his property because in that case opening the door is stupid. Any reasonable person would have called the police then waited inside the house within line of sight of the door (but not directly in front of it), with the shotgun, ready to fire if the person entered. If any interaction is done at all it should be yelling at the person, maybe telling them you're armed and you called the police, although I wouldn't even do that.
Going up to the door and opening it is just putting yourself in further risk and escalating the situation. I don't see how it can be seen any other way.
Here's what I think happened here.. the home owner heard someone at his door (knocking, trying to open the knob, whatever) and assumed it was a burglar. Having been robbed a couple times in the past (if Geosurface's source is correct on this) he was pissed off and wanted to personally run the burglar off or even wanted to actually shoot him/her. After shooting the woman he would have realized she had no vehicle, weapons, tools, accomplices, anything so was probably not a burglar.. and then the "what have I done" reaction would sink in.