Hey Hillcousins,
Thank you for using the Apple Support Communities! We understand you are running into an alert that says your connection is not private, when attempting to use Safari on your Mac. Let's help out, so you can get back to browsing the web.
To get started, we suggest following the steps in this support document: If you can’t open a website in Safari on Mac - Apple Support. If the issue remains, please reply back with responses to the following questions:
-How do you connect your Mac to the internet? i.e. Wi-Fi, Ethernet, VPN, etc. Connect your Mac to the Internet - Apple Support
-Does this alert occur no matter what type of internet connection you are using?
-Does this alert appear for certain websites only? Or, any website you attempt to visit, even Google.com for example?
We look forward to working with you further. Regards.