Are you using Safari?
Try using a different browser when accessing the library's resources.
Is your browser up to date?
If you are still encountering security warnings, consider using the most recent version of the Firefox browser for your library research as there have been fewer issues with the Firefox browser than with Chrome or Safari.
If you get an error message like this one try changing the "https" in your url search bar to "http".
If you're still encountering security and login issues, check your Antivirus software settings. You might have to update your settings to mark the library resources as "safe."