A case in point is POP mail and SMTP in Apple Mail for El Capitan. In case you don't know, POP mail -- or POP3 mail -- is an older email protocol for receiving email. Nowadays, it's mostly replaced by IMAP, but some of us still prefer it. SMTP is used for email sending. For security, both depend on another protocol called SSL, which is used to encrypt email and account sign-ins.
It's SSL that Apple decided to tinker with, perhaps to enforce some obscure requirement that most people considered optional. Anyway, the upshot was that POP and SMTP accounts of mine that had been working flawlessly were suddenly unable to connect.
My emergency solution was to turn off SSL for each POP and SMTP account in Preferences. That also meant changing the ports, since non-SSL email is generally handled by different ones. The specific port changes I made for my service were typical ones: for POP, 995 to 110, and for SMTP, 465 to 587. (For some reason, the SMTP port numbers kept reverting after saving, so I had to fiddle with them and redo them till they stuck.) I also had to change preferences to allow "insecure authentication."
But obviously, this would never do as a permanent arrangement -- and I could do it temporarily only because I was on a secure network. You really don't want to broadcast your email account passwords. So, my next step was to query my email service provider and ask if they could come up with a fix.
I still don't know exactly what the problem was, but this is how they told me they fixed it: "I made a very small tweak to the server config to only allow TLS1 and SSLv3." So, if you have the same problem, you might want to suggest this solution to your service provider. For me, it worked perfectly.
By unwelcome coincidence, my POP account for Google Mail also stopped connecting after the upgrade to El Capitan. In this case, though, it was apparently not so much Apple's fault as Google's. Signing into Google Mail in my browser, I found they had courteously provided an email telling me why my connection had been refused -- an email, of course, that they hadn't let me download.
And what did Google say was wrong? Using Apple Mail for Gmail, I was told, was less secure than using a Google app. So, to keep using it, I had to go to a linked page and tell Google that it was OK to use a less secure app!
Which I did. And now it works just fine -- and as securely as it ever did.