A member's Shopify customer profile and their membership subscription are separate records. Changes made to the store account profile do not carry over to an active membership — Single only honors changes made from the membership account page:

yourstore.com/apps/single/membership#/my-account

This is the most common cause of "perks shipping to an old address" and "renewals billing an old card." Once a fan is on their my-account page, they'll see all of the options below.

Address changes must be made from the membership account page — they then apply to all future perk orders. Updating the address on the Shopify account profile does not change where perks ship, and editing the address on one perk order only fixes that single shipment.

Each membership bills a specific saved card. Members update it from the membership account page, or via the update-payment-method email Shopify sends when a renewal payment fails. Replacing the card on the store account profile alone won't change what the membership bills.

Members can cancel, upgrade, or downgrade their membership themselves from the same page.

Email addresses sync one way, from Shopify to Single. Membership emails go to the email on the member's fan record, while community post notifications go to the member's community profile email — if a member reports emails arriving at an old address, check which of the two needs updating.

They almost certainly updated the Shopify account profile. Send them the membership account page link above.