Taskwarrior is open in as many ways as it can be:

    It is free and open source, using the MIT license
    It uses human-readable text files for storage. It imports and exports JSON, so your data is never held captive
    There is DOM access and a Hook script API
    There are many available free and open extension scripts
    There is Vit, a curses-based UI
    There is FreeCinc, a free online sync service
    There is Inthe.AM, a free online sync service, web UI and iOS client
    There is Mirakel, and Android syncing client app
    There is BugWarrior, so you can import your bug issues from a dozen different bug systems