Giving an agent access is a lot like handing out keys at work. A key to the supply closet and a master key both open doors, and only one of them should go to someone running a single errand.
Muse lets you hand out keys one door at a time. Meta says people choose which apps Muse connects to and exactly how much access it gets. Email is the clearest case: you choose whether Muse reads your mail or can also send on your behalf. You can see the full list of available connectors in your Muse app settings, and Meta says you can change access or disconnect a service whenever you want.
Passwords work differently from what most people expect. Meta says Muse has no visibility into your passwords or payment methods, and any credentials you share with Muse go into secure storage, so Muse can use them without seeing them. Meta also describes a separate Sentinel agent on the same machine: nothing Muse does reaches the internet unless the Sentinel approves it, and it asks you for permission when needed.
Those protections are about how Muse holds what you give it. Deciding what to give it in the first place is still your call, and the simplest rule is to match the access to the errand.
The catch with read access is that reading is still access. An errand that only needs a few receipts still means Muse can see the rest of your inbox while it looks. Connect for the job in front of you, and when the job is done, step the access back down or disconnect the service.
Pick the smallest access that gets the errand done, read before send, and pull it back afterward. Check what Muse found against a record it didn't produce, like your card statement.