There is another thread on this. Apparently nothing to do with iOS 9 as it has happened to others before. I followed a suggestion made for a prior version, but it was a little bit of a pain time-wise.
It said to "Reset All". So I did. Orientation changes worked again - but all my passwords for wi-fi were gone so this wasn't a good thing. I then did a restore from my last backup. Since it was an encrypted backup, it contained my passwords. When done, I had my passwords back and orientation still worked.
It may be that one of the other "Reset" options would work. Or maybe just restoring.