In the movie, Old Yeller is bitten by a wolf, but it's never explicitly confirmed that the wolf had rabies. While Old Yeller shows signs of illness, like becoming aggressive and disoriented, these symptoms are attributed to the wolf bite itself, not a disease.
The filmmakers chose to omit the rabies storyline, likely to avoid the graphic and disturbing elements associated with the disease, as well as the potentially controversial message of euthanasia, which was a significant part of the book's ending.
The movie version of Old Yeller's death focuses on the tragic bond between the boy and his dog, emphasizing the love and loyalty of the dog and the boy's difficult decision to put him down. The omission of rabies allows the focus to remain on the powerful emotional core of the story.