After a lot of trials I finally managed to publish the app from Adobe Animate CC. I tried everything I could think of. I tried removing some ANEs and see if they were the problem.
I then noticed that Adobe Animate would put a <version>1.0</version> tag at the end of the XML descriptor and would not take <versionNumber>9.1.4</versionNumber> into account.
In the end I tried this:
I got to: File > AIR for iOS settings. Clicked on the Languages tab. Deselected the language I had previously selected. Hit OK.
Then: File > AIR for iOS settings. Clicked on the Languages tab. Selected the desired language. Hit OK.
Then: File > AIR for iOS settings. Published the app and everything worked perfectly. The resulting XML would not contain the <version></version> tag anymore and I was able to publish the application from Adobe Animate CC.
So, so, so many bugs. I will try to stay away from Adobe Animate CC Air projects from now on.