Banners do not sway in worlds created before they were introduced.
To replicate:
Start a new world. Place a banner and it will sway.
Then, revisit an old world. Place a banner. It will be static and appear to be stuck in it's furthest swaying position.
Linked issues
Comments
Pretty sure this is a duplicate of https://bugs.mojang.com/browse/MC-63720
My problem is slightly different than his problem. His says that banners don't work in multiplayer. Mine says they don't work in pre-banner worlds.
Happens for me on my server started this summer. No swaying.