MEMPHIS, Tenn.—It seemed a reasonable decision to members of the 99-year-old Union Avenue Methodist Church. With its building and finances crumbling, and just 40 members left, the congregation voted 18 months ago to sell its property to CVS Caremark Corp. for about $2.3 million.

Merging with a nearby congregation, members agreed to use some of the money from the sale for projects such as soup kitchens and missionary work. That seemed to make more sense than spending money on repairs. "Every fourth...