Bsrgvty

I can't comment specifically on ducks, but I will quote the Official Statement on Bread from the Queen's Swan Marker (who has responsibility for swans in the UK):

There has been a great deal of press coverage in recent months regarding the ‘Ban the Bread’ campaign which is confusing many members of the public who like to feed swans. Supporters of the campaign claim that bread should not be fed to swans on the grounds that it is bad for them. This is not correct. Swans have been fed bread for many hundreds of years without causing any ill effects. While bread may not be the best dietary option for swans compared to their natural food such as river weed, it has become a very important source of energy for them, supplementing their natural diet and helping them to survive the cold winter months when vegetation is very scarce.

There is no good reason not to feed bread to swans, provided it is not mouldy. Most households have surplus bread and children have always enjoyed feeding swans with their parents. The ‘Ban the Bread’ campaign is already having a deleterious impact upon the swan population; I am receiving reports of underweight cygnets and adult birds, and a number of swans from large flocks have begun to wander into roads in search of food. This poses the further risk of swans being hit by vehicles. Malnutrition also increases their vulnerability to fatal diseases like avian-flu which has caused the deaths of many mute swans and other waterfowl in the past.

Furthermore, there have been statements made in the media claiming that feeding bread causes angel-wing in swans. Angel-wing is a condition where a cygnet develops a deformed wing. Professor Christopher Perrins, LVO, FRS of the Department of Zoology at Oxford University stated, ‘There is no evidence of a connection between feeding bread and angel-wing; at least some cygnets develop this condition without ever having seen any bread’.

I therefore encourage members of the public to continue feeding swans to help improve their chances of survival, especially through the winter.

See: http://www.theswansanctuary.org.uk/cause/official-statement-bread-queens-swan-marker/

Which I would consider fairly conclusive in the advice to absolutely avoid bread being incorrect. It seems likely that there are better things to feed the birds than bread (it is easy to buy special bird food, which my wife does), but that is not the same as saying that bread is bad.

To address the feeding of ducks:

Ducks Unlimited Canada has this to say:

I’VE HEARD THAT FEEDING DUCKS BREAD IS BAD. WHAT SHOULD I FEED THEM?

DUC does not recommend feeding ducks. It increases the chances of
negative human/wildlife encounters and can make them dependent on
people for food.

The Canadian Wildlife Federation has a similar suggestion:

Can I feed ducks bread?

The short answer to this is no.

Ducks naturally eat a nutrient-rich diet that may consist of insect
larvae and other aquatic invertebrates, small fishes, amphibians, as
well as seeds and aquatic plants. Bread and similar products such as
chips, donuts, popcorn and crackers provide very little nutritional
value.

Ducks that are regularly fed bread can become malnourished, aggressive
towards one another, may lose their foraging instincts and can lose
their natural fear of people.

Also, bread that isn’t eaten can result in nutrient build-up and
increased algae growth.

Feeding wild ducks is a practice CWF does not encourage. They may look
cute, and a bit of bread might get them flocking towards you, but
feeding them is doing more harm than good.

So, at least over on this side of the pond, the experts seem to be recommending that humans don't feed anything at all to ducks.

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:

1. I'm having trouble finding any scientific resources that back up this claim.




2. Claimants don't seem to be providing their own references.




3. 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.

The problem of undigested bread

Bread may be bad for ducks, but not necessarily for the reasons stated

The claim in the question concerns whether bread directly causes diseases for ducks and swans. This claim has been addressed by other answers. However, there are other, indirect effects to consider, regarding the wider effects on the pond ecosystem (which, indirectly, will be bad for ducks).

In many urban ponds, ducks and swans get simply fed too much bread, and bread is left uneaten. Undigested bread will rot, attracting surface algae which are toxic to fish. It also attracts rats, which may carry disease vectors dangerous to both ducks and humans.

From BBC News:

Now conservationists are warning that undigested bread sinking and rotting can create wider havoc.

The Canal and River Trust says that it can encourage bacteria and algae which can poison other species as well as attracting vermin.

Rotting bread exacerbates naturally occurring surface algae - which can give off toxins damaging to fish populations and create a stench for humans - by releasing more nitrates and phosphates. It also denies sunlight to underwater plants. And the bread eaten by birds creates more faeces, which has the same effect.

The nutrients can also encourage filamentous algae, which grow upwards from the bottom in chains or threads. The algae can slow down river flows, further deadening the environment.

"Of course, bread's not the only thing that causes the problem," says Richard Bennett, an environment manager at the Canal and River Trust. "It wouldn't matter if you fed ducks in a clear, nutrient-free environment like an upland stream, but people are more likely to do it in towns and cities."

Decomposing bread creates [sic] bacteria and attracts vermin, especially rats, whose urine transmits Weil's disease, which can be deadly to people.

Wet and rotting bread can be a home for a mould called aspergillus, which can get into ducks' lungs, killing them.

So, the claim in the question is partially correct. There are good reasons why feeding bread to ducks may be bad for them, but the reasons stated in the claim are not supported by available evidence.