My large, international employer supports employees volunteering in our local communities, even allowing us to spend a certain amount of work time on such projects. My local office of about a dozen people was recently talking about doing something as a group, and somebody offered to organize a project. (That happened while I was on vacation, so I don't know the details of that conversation, but I'm on board with the general idea.) A group project, in addition to helping the local community, is an opportunity to do something valuable together as a team that isn't work. I think there's team-building benefit to that.
Here's the problem: the specific organization the person contacted is problematic for me because their work is strongly bound up in a religious mission that I cannot support. Their religious goal is front and center in all their publicity, their motto, their client interactions, etc -- bringing the light of (name) to the world, that sort of thing. I'm happy to do the type of work they suggested, and I'm always glad to hear of religious groups that act on their faith by doing things like feeding the hungry -- but I can't be part of a project that promotes their religion, which their work does pretty blatantly. Participating in that way is a violation of my religion. (Please just take me at my word on this; I'm not trying to start a religious argument.) I am certain that this possibility did not occur to any of my coworkers.
The project got far-enough along while I was away that I would feel awkward saying "er, could we do something else instead?". Because we are a small group, it will stand out if I don't participate. I'd also rather not lie about being busy; I don't like lying, and it will also probably be pretty obvious because it's a work-time project, not an evening or weekend. If I organize a different project (which I'd rather not do, but could do if necessary), I worry that it looks like I'm stomping on (or at least wasting the time of) the coworker who already made these inquiries. If I tell that coworker why I'm uncomfortable, I risk an uncomfortable conversation in the workplace. I'd also like to avoid giving the impression that I don't care about helping my local community -- I do, but not like this.
How and with whom should I bring this up? We're all peers except for one manager (who is not my manager; mine's remote). We all get along well and like each other, but we're coworkers not close friends. They are all aware of my (minority) religion at a surface level but are almost certainly unaware of the problems of involvement with this other religion. (After all, most people never have reasons to think about stuff like that.)