I don't like getting involved supervising a staff member who is not one of my direct reports. I prefer to let the supervisor handle it. I have a three-pronged strategy: 1) Ignore, assuming the staff member will handle it properly; 2) If the issue is not resolved, ask the staff member and supervisor what the status is; 3) Get involved in the solution. So, I ignored the first one. After the second email I sent an email to my staff guy and his supervisor asking, "What's the status on this? Do you need my help?" I want to make sure my words to my staff don't assume they haven't dealt with it. I also want to offer my help: sometimes staff feel unequipped to deal with these kinds of situations. I never, never want my staff to feel like I'm not supporting them. I back them publicly and then deal with them privately.
My staff person just emailed me 5 minutes ago and told me he had in fact emailed this guy & had tried to call him. If I had expressed doubt earlier that he was responding properly, damage in the relationship would have resulted. I gave him two options: 1) copy the guy (and me) all the emails, asserting he had responded, and then call him and try to get a face-to-face with him; 2) Just call him and try to get a face-to-face. I suggested he could do it solo or with his supervisor. At writing, not sure which he will do. At this point, I have no intention of responding directly to the congregant.
Irritable church folk can be land mines: handle them and your staff carefully. Don't slug the member in the nose and don't cut your staff off at the legs! A measured response is best.