Play YouTube in the background on iOS

  1. Install Shortcuts app if you don't have it already:

  2. Open Shortcuts app, go to Gallery tab and install any shortcut. This is needed for the next step, you can remove it later.

    Shortcuts gallery
  3. Go to Settings → Shortcuts and enable "Allow Untrusted Shortcuts". This is needed to install third party shortcuts like Listenbox.

    iOS settings
  4. Install Listen shortcut

  5. (Optional) Install Listen Later shortcut

Now you have Listenbox in your share sheet. Tap this button and choose "Listen" from the list:

iOS share

If you don't have a podcast app, Overcast is cool: