This is a tough dilemma. I have had people quit on me and I have understood as there's usually some amount of improvement in their life for the change (more pay, stability, responsibility, etc.). I'm usually happy for them. I appreciate it when they are open enough why they are leaving as it prevents most speculation and gossip among those who stay. For that reason alone I'd give a substantive reason, but I don't work in a small values driven environment.
My wife worked non profit for 10 years before making a huge career shift into a completely different sector because it was taking too much of a toll on her. Her immediate supervisor understood, but her peers eliminated her from their social circle. It's a weird mentality because they for sure thought she was abandoning them because she wasn't committed enough or something (obviously), but it started a wave of people leaving the org due to a pretty toxic environment. She is still close (familiar colleagues but not friends) with her old supervisor and execs but not those peers, but never really fit in in the first place with them. I think several people are in a better/happier place knowing that it is actually ok to leave; those who held it against her eventually left too, but they all still regularly support this org and believe in the value it brings to its community.
I think I'm telling you this story because you will probably burn bridges with some, but if you do it professionally, usually the more seasoned folks know that people come and go. Some are "lifers" at these orgs, others aren't.
Are you planning on providing some future support to them? I think you can quash any notion of you not believing in the cause by other forms of support (volunteering, monetary, services given in kind for special projects, etc.)
I believe you can come up with a way to tactfully say you need a break as it sounds like it is something you want to do. It just seems like you're too close and every little thing is getting to you, which screams that you need a break. We've all been there. I think it says something about your commitment that you haven't been interviewing for a new job. Use that to your advantage.
If I think of a ringer thing for you to say, I'll post it, but you are probably going to be the one who knows what's right.