Maybe the neighbors weren't told about an "armed man." Maybe they were only hurriedly told, "Elizabeth is missing!" Maybe some of the neighbors were themselves armed. Maybe the fact that they thought Elizabeth was at the mercy of a man with a gun made them all the more frantic to find and rescue the helpless girl.
We're not even sure when it was that Ed supposedly found out from Mary Katherine that the man was armed. Remember he said that at first he'd thought she was dreaming, but then he looked for Elizabeth and didn't see her. Maybe at that point he took off out of the house, just knowing Elizabeth was gone, and didn't get back until later to hear the details of what had supposedly happened.
I am not sure I believe the man was really armed. You say you are not sure of that either. Maybe some of the neighbors weren't sure of it, either.
Remember when those searchers, the next day, reported seeing the man and then hearing gunshots? People converged on the spot where the searchers allegedly saw the man. Doesn't sound like they were overly concerned about their own safety. Some people act too quickly in an emergency; most people wouldn't want to be seen turning tail and running away to just hide in their house and refuse to help some poor 14-yr-old girl. Also, I'm sure they all thought that quick action might solve the whole thing before Elizabeth came to harm.