Does that kind of thing work on Google Docs?
I'm not positive but I'm pretty sure it does. Unfortunately this organization couldn't get recognized as a non-profit so Google Docs was too expensive for them. Office 365 is offered through Tech Soup who did recognize the church as a non-profit, which got them the service for very little.
I think there's a way you can set up one account and share that contacts folder or a sub folder of contacts to everyone. Even then I'm not sure that will show up on mobile devices. Doesn't necessarily need to be a whole new one but that would be the cleanest way in case the user leaves.
That's basically what I've been reading as the only solution. I'm not sure if the contacts will show up on mobile or not.
There's also a way to set up "public folders" inside a public mailbox. I've set up both but haven't created the contacts or calendar entries yet. It's the perfect way to do this sort of thing, because I can control permissions from the admin panel and it'll just show up on the appropriate users' systems... but... IT WON'T SHOW ON MOBILE! This is just stupid.
There's also the global address list, but as far as I can tell there's no way to edit that beyond adding and removing users from the organization.