For many years mac computers using parental controls have had difficulty accessing secure (HTTPS) sites. The generated errors appear as cryptic SSL errors. These steps should get your mac successfully connected to google services such as gmail.
My daughter has recently started learning online through khanacademy. Initially, we had great difficulty trying to login through her google account. The initial errors were of the SSL variety, and Safari reported a generic inability to “establish a secure connection to the server.”
The parental controls built into OS X has never navigated secure sites correctly. Typically, this can be corrected by adding the troublesome site to the Website Restrictions exclusion list; however, since google bounces through such a great number of servers, it can be more difficult.
1. Open Parental Controls in Preferences
2. Select the account to change and unlock if needed to make changes
3. Click the Web tab and click the Customize… button.
4. Under Always allow these websites: add the following entries:
https://74.125.45.100
https://1e100.net
http://1e100.net
https://appengine.google.com
https://google.com
Once the entries are in the system, press the OK button. You may need to restart your browser to notice the changes.