Update: Apple confirmed on its iCloud status page that Find my iPhone is back to normal:

The Find my iPhone iOS app has been updated with a new iOS 7-style icon while the rest of the UI remains the same. This icon is the same as the one found on the updated beta.icloud.com website:

However, many are noting that you cannot log in to the new Find my iPhone app without having a developer account:

Meanwhile, Find my Friends also received a small update to fix bugs, but the icon and UI remain the same. The app is functioning properly.