RFID wallets are indeed capable of going through airport security without any significant issues. The amount of metal in these wallets is usually too small to cause any major disruptions during security checks.
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Money belts and neck wallets — those flat, cloth pouches that fit under your clothes — are the traditional ways to carry money safely while you're traveling. They're meant to escape the notice of pickpockets and muggers, and some even have RFID blocking to keep your credit card and passport information safe.