@phesse , by any chance, are the non-admin users all using the Safari browser with default "Allow from websites I visit" setting for cookie policy? We've seen the blank screen before in that scenario.
LTI tool providers ideally will accommodate Apple's different implementation of cookie policy by rendering a minimal interface which users interact with in order to set a persistent cookie and reload the page. After that reload, the LTI tool can look for the persistent cookie and set up a session.
To work around this without the LTI tool being changed, you could advise users to switch to "Always allow" or to try a different browser.