I just created a "shared theme" for my organization in the AGO settings. Now when creating a new WebApp Builder application, the Theme tab is blank. I would understand if the setting of a shared theme would not allow for any changes to the Style section, but why can I not adjust the Layout or most importantly switch between themes? I now seem to be restricted to the "Foldable Theme". The documentation I've read about setting up shared themes states that it will become the default but can be over-written by the user if they desire. Is this a glitch?
The problem only affects newly created apps and simply removing the shared theme does make these settings reappear when creating a new app.
There seems to be issues with shared themes. I would contact esri tech support.
This was happening to me a few weeks ago, but it resolved itself a few days later for unknown reasons.