If an app has two menu icons and user has decided that both should be hidden, only one is. Example: Microsoft OneDrive is singed in with both Personal and Work accounts If user decided to hide the OneDrive menu icon app, only one is hidden while the other remains visible.
I now have almost the opposite issue on my Mac (OS 10.15.4 Catalina, Toolbox 3.9.0) When I turn on Hide Menu Icons, the OneDrive icon will completely disappear from both the visible and hidden toolbar. It will reappear after I quit Hide Menu Icons. Since OneDrive has the habit of getting stuck, I frequently need to use that icon, which prevents me from using this Toolbox feature.