It depends on the backup type.
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​File Backups:

Set up a user with READ access on the folders that you need to back up, and just WRITE permission on the operations directory.

Note: SimpleBackups does not required root or sudo to run, so you can completely contain the scope of operation.

The operations directory is where SimpleBackups stores files required for its operation. Example, backup log during a running backup, rclone which is used to send backups to your storage.

​Database Backups:
Set up a user with READ access on the databases you need to back up.

Cloud Storage:

You can give SimpleBackups as little permissions as possible on your storage. It depends on the storage, but just read/write to where backups should be stored it fine. You may also connect a read-only storage and do not provide SimpleBackups with a write permission if you prefer.