With the default settings, inboxy does not handle any personal or sensitive data.
However, if you choose to customize your extension settings, inboxy uses the Chrome Storage Sync API to sync settings to browsers that you're logged into.
In particular, the settings allow you to specify a list of labels to bundle (whitelist) or not to bundle (blacklist), instead of defaulting to bundling all labels. The list of labels may contain personal or sensitive data—for example, you might have a label where the text is your name. To maximize protection of your data, you should either:
inboxy's usage of data adheres to the Chrome Web Store User Data Policy, including the Limited Use requirements.