I have an iMac, 2015, running OS 10.12.5 and the latest version of Opera.
I cannot determine how to rearrange the order of the bookmarks in the folders in my bookmarks bar.
Lets say that in the Opera sidebar I go to All Bookmarks > Bookmarks Bar and then to the folder titled Apple and rearrange the bookmarks therein and then close the Bookmarks sidebar, if I then click on the Apple folder in the main window of Opera, in its Bookmarks Bar, the order of the bookmarks in that folder has not changed.
Whether from Bookmarks manager or from Bookmarks bar your custom arrangement should be reflected.
Try to use Sort alphabetically and then try to reorder at your own taste.
Windows 10 (x64) | Anniversary Update
Opera Stable · Beta · Developer
Test profile | Back up Linux · Mac · Win
Strangely, in the Bookmarks manager, I found TWO folders labeled Bookmarks Bar.
The topmost one, immediately under All Bookmarks and a second one which became visible when I tapped the triangle to close the All Bookmarks.
The arrangements of the bookmarks in the Bookmarks folder immediately under All Bookmarks did not reflect the arrangement of the bookmarks in the Bookmarks Bar; the folder labeled Bookmarks Bar at the very bottom of the Bookmarks Manager did, so I simply deleted the topmost Bookmarks Bar folder and now all is well.
The previous Dropbox link did not work; this one should https://www.dropbox.com/s/w9w6qs9vvn5kvs6/clip_2.png?dl=0
If you have imported your bookmarks, maybe that is the reason of having two Bookmarks bar folders.