Yes, we have data that we are not currently sharing in our public web apps because we cannot hide the table view in the source web map. I know how to hide table accessibility in web apps (I'm using WAB Developer Edition), but the web map itself is still public and therefore searchable/discoverable via ArcGIS Online searches.
I'm sure it seems odd that we would be willing to expose data via a click in the map, but not in a table. Without going into specifics, we are concerned that making the data visible in an aggregated format will lead to misuse of the information.
Thank you for confirming that table view cannot be disabled in a web map. Alix's response suggests that there is a way to set up a web map so that it is only be available through a published web app; is that possible? I haven't found any documentation online that offers a workflow for this. Or perhaps there is a workflow that would meet our needs via Portal?