Android Rebuilds, which provides freely-licensed Android development tools, starts a public repository with F-Droid :)

https://mirror.f-droid.org/android-free/repository/

We're now trying to make it usable for sdkmanager, which should vastly ease the installation process (download what you need, rather than huge mono-version bundles).
Help is welcome to format the repository and possibly adding a way to override sdkmanager's default repositories, join the conversation!

https://forum.f-droid.org/t/call-for-help-making-free-software-builds-of-the-android-sdk/4685