The same way everyone else does: encrypt the data using a secret known only to the customer, isolate internal systems that have access to the decrypted data so that no one person can ever access that data on their own authority, and ensure that whatever procedure does permit access with the requisite authority creates a robust audit trail. If security really matters, the whole system and its logs should be regularly audited by an independent party, too.

You have to have some sort of trust, because obviously if everyone in the company is crooked then nothing but encrypting everything client-side using auditable code is bulletproof. But you can certainly engineer systems so that access requires multiple people's consent and gets securely logged, which would eliminate casual snooping and provide robust evidence for legal action in the event of collective abuse.