I really don't think email providers have anything to do with the problems that are happening here zeugmatis, I think these are Apples problems... caused 100% all by them and their developers! In my case and from what I can read, these email accounts that the El Capitan upgrade messed up all worked for people before the upgrade so I really don't know where you are coming from on that one!
Moving on...
I had most of Sunday available to put my feet up this weekend and decided to have a look at a second attempt at upgrading to El Capitan, now knowing how easy it was to wind my computer back and after thinking about the problems, so this is what I did to get my laptop and Mail app to work with El Capitan, just a word of warning though, it was a bit of a laborious process considering I have 12 email accounts but hopefully most people don't have as many and so a little less time consuming but of course if all goes well then it is fully worth putting in the effort, so this is what I did to get things to work:
1) Opened Disc Utilities and selected to Fix permissions
2) Went to Mail app and opened Internet accounts (I had to select to delete an email account to get this option then not actually delete the account when Internet accounts opened)
3) I deleted every Notes account for each email that the OS had created without my knowing, I don't use them.
4) Close the Internet accounts window.
5) I opened each email account and took screen shots of: Account information tab window, Advanced tab window. So I had a copy of all the settings that actually worked on my email accounts.
6) Opened the SMTP server window and took screen shots of the Accounts information tab window and Advanced tab window.
7) Moved all the screenshots into a folder on the desktop.
8) Made a complete backup on Time machine, took about 10 minutes or less.
9) Closed every application that was running and restarted the mac.
10) I had ran the upgrade to El Capitan before and wound back to Yosemite after the issues I had a few days ago so I still had the Installer 'Install El Capitan' in the Application folder it was download to, I double clicked it to run it.
11) I followed the prompts I entered my password and ID for iCloud as asked by the installer, I noticed this time it asked if I wanted to confirm File vault setting to encrypt, I deselected the checkboxes for file vault option as I did not want to encrypt my files, at least not for the moment. I do not remember the installer asking me this option the last time I tried to update to El Capitan... I wonder if it just tripped over that and encrypting things was the problem, anyway.....
12) After the computer restarted and was ready to try and open apps I disconnected for the internet so Mail didn't connect to my server for emails, I did that because my server manager said it was bombarded with connection attempts by Mail the last time with wrong passwords and port information causing the server to block my IP address... 3 times in about 20 minutes.
13) I opened Mail app and deactivated all my mail account accept one.
14) I checked the settings for that account 'especially port numbers, if the POP and IMAP accounts where still POP and IMAP accounts' corrected information that was missing or not matching the screenshots for that account then closed the account window and saved on any prompt, not forgetting SSL settings of course along with making sure you enter the correct passwords for the account.
15) I opened Mail preferences and then selected the same account then checked that the information for that account had actually been saved.
16) I closed the account window and connected to computer to the internet and tested that one account for sending and receiving.
17) When that account worked I then did the same for each of the email accounts one at a time.
After the above process I have found no issues with El Capitan 'As yet', I worked with it for a couple of hours in the evening, an hour this morning and another hour this afternoon and so far so good with email accounts seemingly keeping the stored information and working.
I hope this is useful for anyone attempting the upgrade or feeling up to trying a second attempt, good luck.