I have some people in our Good Sam group who volunteered with Habitat for Humanity for several years while full-timing. They would work four or five one month projects a year in return for an RV spot at various locations across the country.
One of the things they really enjoyed was the faith based nature of Habitat, with the morning devotionals and the connection with local churches where the projects were located.
You might want to look into that.
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But as mentioned above - most churches are welcoming to visitors, and you can choose to become involved and to which degree.