Are you referencing the Infusionsoft Sidebar for Email, or Infusionsoft Gmail Sync? There are 2 different offerings that Infusionsoft have. I ran a test with one of my non-admin users on both ‘Sync’ and with ‘Sidebar for Email’ and was able to get logged in. Off hand it doesn’t sound like there is a pop-up blocker in play here, as you reference being asked to allow permission for the sidebar to load.
If you are still experiencing this, you may want to give the support guys a ring at 1-866-800-0004 Ext 2, to run through a few steps, because there isn’t a specific permission in the user permissions set to block access to Sidebar for Email or the Sync sidebar.
If you can identify which sidebar your users are attempting to use, the support team should be able to run through some tests, and pull any access logs to see what may be causing your users to not be able to access it.