The more I thought about it, the more I realized that the idea that wild birds regularly consume chewing gum doesn't quite hold water. Chewing gum doesn't "look like bread" any more than it looks like a rock on the sidewalk-- and a quick peck will reveal that it has a rubbery texture and likely unpalatable flavor. If birds ingested everything that remotely resembled bread, they would be consuming pebbles, vermiculite, paper wads, and cigarette butts with regularity. No animal would do well if it ate everything that in some way resembled a man made food product.
After doing a little research, I found that experts in wildlife biology agree with me when asked specifically about the safety of littered chewing gum for birds. In 2009, Ern Tobias, an animal expert at Lake Tobias Wildlife Park, told CBS 21 News that birds will generally peck at a piece of gum once or twice before realizing that it is inedible. After realizing that it isn't anything tasty or nutritious, they will turn away and seek something else to eat. He ultimately disagreed with the notion that chewing gum is dangerous to wild birds.
However, CBS 21's investigation did find some evidence of at least theoretical risk. Troy Stump, director of ZooAmerica, told the authors of the channel's "Legit or Lie" program that it's "conceivable" that a small bird might eat a very large piece of gum and choke to death. He notes, though, that gum itself "is not and would not be a fatal substance for birds," since most would be able to swallow it inconsequentially, just as humans do.
While chewing gum may not be a direct threat to the health and safety of wild birds, it's still prudent and polite to toss your gum in the trash can, where it belongs. Litter of any kind-- especially the kind that has been in someone's mouth-- is unsightly and unsanitary, even when it does not directly jeopardize wildlife. The sidewalk simply isn't the place to get rid of a wad of chewing gum.