Hi Wayne,
Customization is limited when it comes to the FileContent browser UI.
You can configure the toolbar to not display things like the folder tree button for the user to toggle, but this would apply to everyone, not just some users:
https://www.labkey.org/Documentation/wiki-page.view?name=fileManagementAdmin
What do you mean by "the home folder in the tree"? When a user is viewing the Files Web Part or the FileContent browser, they are viewing the files that pertain to the specific container they're in. For example, if I was in a project called /MyStudy, the Files Web Part would only show me the file repository for /MyStudy and nothing else. If you were in a subfolder under /MyStudy and the path was /MyStudy/MyAssays/MySubFolder, you would still only see the File Repository under MySubFolder and also /MyStudy wouldn't have visibility into MySubFolder or even MyAssay since all of the respective repositories are siloed.
Regards,
Jon