I would say they are quite important, perhaps even crucial to the well-being of a community because of the social services and social connection they provide. Isolation is devastating to individuals, communities, and our capacity for representative government. The government would also have to pick up the tab for additional social services if not for churches.
How important are active churches for the overall well being of a town or neighborhood?
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I agree with @Stephen Jaques2: I think active faith communities can be a tremendous boon to the overall strength of a town. They provide connection and services, as Stephen said. I've also been thinking lately about how churches sometimes control a significant amount of land. In the same way Strong Towns encourages cities and businesses to think critically about how they develop a piece of land and build on it, churches have a responsibility to do the same -- a responsibility (in my opinion) with a serious theological basis.
My answer won't surprise Al Doyle3, who is a longtime friend and collaborator doing awesome work in the Pacific Northwest.
Here are a couple Strong Towns articles that get into just this topic:
This question has multiple answers depending on the church, leadership, congregation, etc. One church in Atlanta built a tiny house development for women escaping the sex trade. https://www.fox5atlanta.com/news/tiny-house-community-being-built-for-women-who-escape-the-sex-trafficking-trade3
A local church in my town purchased a former drug house and has converted it into a duplex that will be used to house people while they get back on their feet. In these regards, the church is helping to shape the community by serving people, loving their neighbor, eliminating blight, increasing property values, etc.
The opposite is also true where some churches are vacant or abandoned or their parishioners have no connection to the neighborhood or people around where they attend church. This leads to a disconnect and doesn't benefit the overall well being of the community.