I had this problem on my iMac with 13.7: Safari would frequently report that it couldn’t establish a secure connection. 13.8 seemed to fix it on that machine.
But on my MacBook running 13.8, I got that error message trying to get to the NYC voter registration site:
https://voterlookup.elections.ny.gov
When I turned off the web shield, it worked. Turned the shield back on, no connection. Tried that a few more times just to make sure.