Russian athletes can compete as neutrals if they have not tested positive for performance enhancing substances.
Biles left the team after her vault on Tuesday.
Gallegos-Main quickly removed the comments from her social media after they met with backlash.
Sweden won the match 3-0.
Both the men's and women's teams have come off a string of losses in the early warm up games.
Richardson was expected to be a challenger for the gold medal in the 100m sprint.
Springsteen will be joined by Ward, Farrington and Kraut.
Richardson tested positive for cannabis at the US Olympic Trials in June.
Richardson was a favourite to win the gold medal in the 100m sprint.