I am having the exact same problem -- I think it is an issue related to the upgrade to MacOS 10.12 (Sierra) because I did not have this issue prior to the upgrade.
Interestingly I can successfully access a number of CAC-enabled websites such as: hrc.army.mil and https://web.mail.mil.
However, I cannot access https://www.us.army.mil. When I try to login to this AKO site, I can select my CAC, input my CAC pin, and then I get an error screen that says "Safari can't open the page ... because Safari can't establish a secure connection to the server 'certificate.us.army.mil."
Can someone help us?