Safari users sometimes get "Connection is not Private" error when accessing my site (which uses NGinX and Let's Entcrypt).
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You are sending the leaf certificate alone. You need to send the intermediate(s) as well. If you use certbot and your app supports it, send fullchain.pem. If you have to use cert.pem, then you have to use chain.pem as well.
I was able to improve the configuration, as per your suggestion, and am now getting a better result on ssllabs. Hopefully this will also resolve the issue with Safari browsers, Thank you so much.
We activated both sites simultaneously in IIS before launching LetsEncrypt (via WinAcme 2.1). This achieved the goal, both sites added to the Subject Alternative Name (SAN) List.