WAT DHAMMAKAYA, Thailand—The spectacular growth of the futuristic Dhammakaya Temple here is raising some awkward questions about how Buddhism should adapt to decades of pell-mell growth that have transformed the economies of Asia, the faith’s heartland.

Visually, the temple, nestled in Bangkok’s industrial northern suburbs, is like no other. Its stupas, or Buddhist spires, are shaped like flying saucers rather than the ornate pagodas dotting the rest of Thailand. The largest is sculpted from 300,000 miniature Buddha statues....