tl;dr- I haven't been able to actual evidence of the claim that consuming bread causes angel wing in ducks, and an expert claims that there isn't any.
Apparently the main claim against feeding ducks bread is that it gives them angel wing. However, I'm not immediately finding any evidence for this on Google; most results appear to be unreferenced political advocacy.
A few sources seem to suggest that this claim came from "Geese Peace". Google turned up this from their website:
No feeding Program
Recreational feeding of Canada geese at GeesePeace program sites should not be permitted.
When geese are fed they approach people who may be afraid of them.
Feeding goslings may cause “angel wing” which is a deformity of the wing caused by rapid growth of feathers as result of a high protein diet (bread, corn)
Feeding geese causes the geese to congregate in the feeding area which then increases the geese nuisance level in that area and causes geese to become aggressive as they fight over the food.
Feeding bread, corn or other “treats” may keep them from going on a molt migration.
–"No Feeding Program", Geese Peace
However, as with other sources, I'm not seeing any references to a study to back up this claim – it's just stated as though it were established fact.
Chris Perrins, who seems to be an expert on the topic (and has been dubbed "Warden of the Swans"), claimed that there isn't any evidence:
Zoology professor Christopher Perrins said there was no evidence of a connection between bread and angel-wing, and some cygnets developed the condition ‘without ever having seen any bread’.
–"Swan rescuer says bread warning is 'fake news'" (2019-04-09)
Likewise, a recent blog post (2018-12-19) claims that there's no study or paper to be found:
Whilst doing a bit of research around this contentious topic, it became quickly apparent that there is no study or paper to find, which conclusively proves that feeding bread to waterfowl is the sole cause for the development of angel wing deformities. Despite this fact, most wildlife and waterfowl experts seem to agree that the overwhelming cause of angel wing is an unhealthily high protein and / or carbohydrate based diet. Unsurprisingly, it was not difficult to find plenty of advice and warnings suggesting not to feed bread to birds, and in particular not to waterfowl. However, with all the advice being provided, no scientific references were given, which would certainly help to clarify and understand the situation.
–"Thoughts About Bread And Angel Wing Deformities" (2018-12-19)
They do their own analysis (with references), and conclude:
So What Is The Conclusion?
There is no definite answer or absolute truth. As with any diet, it is important to feed a balanced diet and to feed in a responsible way. This means that neither bread, swan pellets or any other high energy food like chicken crumbs should be exclusively fed to waterfowl, in particular not during their first four weeks of life. However, it also means that bread and swan pellets can form part of a balanced diet, when fed responsibly, in addition to wheat, cereals, grains, leafy greens and dried grass. Birds should always only be fed on the water and only small amounts should be given to make sure that all food has been eaten before giving more. Mouldy food should never be given.
–"Thoughts About Bread And Angel Wing Deformities" (2018-12-19)
So:
I'm having trouble finding any scientific resources that back up this claim.
Claimants don't seem to be providing their own references.
An expert claims that there isn't any evidence.
It's hard to guess where this claim may've originally come from, but it doesn't seem to be backed up by a scientific study.