For mainland Chinese, a visit to Hong Kong feels like a voyage back in time. At home they spend weeks without a visiting an ATM or a bank. They use mobile wallets to pay for meals, bills and cabs, or even donate to beggars; they invest their unused balance in money-market funds, still using their smartphone. But when they cross the border into the special administrative region, they leave such conveniences behind. Cabs accept only cash. Not all small shopkeepers take cards, and they often...