Habitat loss is a big factor in bird populations struggling. Birds use feeders, when there aren’t the insects they eat, due to use of pesticides on farm land. We had a family of bull finches for years. Some new houses were built on agricultural land - we’ve not had a bull finch for years. We guess they lived on that land.
Some finches, especially green finches and gold finches have been impacted by a disease, which occurs in part due to dirty bird feeders. We used to get loads of green finches and 90 gold finches at a time. We are lucky to see a green finch now, and only get a few gold finches. (We wash our feeders regularly).
Feeders can affect the structure of wild bird populations, because birds, who use feeders get a boost to their health and sub optimal birds survive the winter, who may otherwise have died. They can expand their population at the expense of a non feeder species.
Feeders can attract birds of prey - we get sparrow hawks doing a sweep of our garden regularly. We have even had a peregrine a few times.
The corvids used to attack birds of prey, like buzzards round here, long before we saw our first red kite.