And the name of the gremlin is...
Winpcap.
Thanks to
nevr44 for reminding about that treacherous little weasel which finds its way through other programs.
The problem is that it generates several files with the names other than "winpcap". Luckily, Win 10 search can find them.
Files deleted, registry checked.
And I am able to join 4.14 servers. The problem is resolved.