Big Bird isn't alone. As of 2024, five avian characters have earned the 2,700+ terrazzo-and-brass stars on Hollywood Boulevard:
The prompt's premise ("Big Bird and [one other] are the only two") is incorrect. If counting only birds (excluding Mickey), there are four: Donald, Woody, Big Bird, Tweety. If counting all "animal characters," Mickey makes five. No other birds (Road Runner, Daffy, Chicken Little, etc.) have stars as of 2024.
Walk of Fame stars require: nomination, committee selection, $75,000 sponsorship fee (paid by studio/fan club), and attendance at unveiling. Animated characters are eligible under "Television" or "Motion Pictures" categories. The bird cluster reflects the golden age of American animation (1930s–1950s) and Sesame Street's cultural weight.
So: four feathered stars (five if you count the mouse). Big Bird has company—and he's in good feathered company.