Like a church? A synagogue? A mosque? That fits the definition exactly. It seems like a substitute for a house of worship for people who do not believe in God.
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I might be very misinformed about how church works, but I think that coffee shops fill a very different niche. History kinda supports this: coffee shops became valuable places of business and occupied the 'third place' role even in extremely religious places and times (I'm thinking of Lloyd's specifically, and 17th and 18th century coffee shop culture as a locus for business ventures in the Netherlands and England).