Access to the site (https://tenant.sharepoint.com) was disabled for tenant users, since it is a site that is not being used, only global administrators have access to that site. With users who are global administrators the webpart works without problems. The webpart does is to look for the user's photo to display it, but since the user does not have access to the site (https://tenant.sharepoint.com), the webpart fails. We gave access to the site (https://tenant.sharepoint.com) to a user with the problem, and immediately the web part worked correctly. So we are checking if the user's photo can only be obtained from the tenant's site (https://tenant.sharepoint.com)
It's a bit too late to help you but it might come in handy for others.
_layouts/15/ is a folder inside the server (C:\program files\common files\microsoft shared\web server extensions\15\template\layouts\) and it's available for all of the site collections.
So, you can access it from any site collection that the user has access to.
