I agree with John, I never got any indication of gay from the song.
Seems most assumed what was thrown over was an very premature or aborted baby named, or would have been named Billie Joe.
Note in the lyrics Billy Joe is male (at least in the South) Billy, Bobby, Eddy, Robby are male. Billie, Bobbie, Eddie, Robbie are female. The person in the lyrics is Billy but in the Ode to its Billie.
What did the rev. see them throw over? If close enough to recognize their faces he should have recognized flowers. And "they" were throwing something over and if wrapped it would not be possible to tell what it was.
She is now throwing flowers into the river....much like taking flowers to a grave? I would assume Billy Joe's body was found and buried elsewhere so there would be no need to take flowers to the bridge for him. It would be the only known grave for Billie.