In this society, many object to women showing themselves off in public, while others dislike the game they play because of its association with the US troops who invaded the country more than two years ago.
Softball, a form of baseball, was banned under ousted president Saddam Hussein, who viewed it as a product of US imperialism.
Now, a year after it first took off at Baghdad's sports academy, women have formed six teams who compete in a nationwide championship.
But training at the Baghdad academy is difficult - the field is rough and the grass dying; the sun beats down harshly and the equipment, donated by neighbouring countries, has seen better days.
A dozen women, wearing blue outfits and with their long hair hidden under baseball caps or scarves, begin exercises with stretching and a short run.
"Because of the heat, we must train early in the morning or late in the evening. For the girls, those are dangerous times. They can be kidnapped or killed"
Ismail Khalil, trainer and head of national baseball federation
"I love this sport because it's new," said 19-year-old Zina Tariq.
"But it requires a lot of effort and training," said the student whose father was a famous football player in the 1960s.
"The team is like a family. We're united by real friendship and passion," said Lamis Wail, 21, from behind a pair of black sunglasses.
"At first, we didn't even know the rules of the game, nor even how big the field was supposed to be," she said.
The women must run a daily gauntlet of car bombings and shootings to turn up for training.
"Because of the heat, we must train early in the morning or late in the evening. For the girls, those are dangerous times. They can be kidnapped or killed," said their trainer Ismail Khalil, who also heads the national baseball federation.
The girls train every day under
the threat of attacks
To reassure the families, the federation has provided buses to ferry the players to and from their practice sessions.
But Zikra Jasim, 20, considered the best player and who wears a veil while playing, said: "Our parents are worried even if things have improved because of the buses.
Teammate Tariq added: "I'm afraid the girls will lose heart if something happens to one of them."
Lamis Wail says she has been insulted in the street because she plays sports. But "I've chosen to study sports and my family supports me", she said.
Amir Jabbar, the deputy chairman of Iraq's Olympic committee which finances the new sport, concedes there are "negative reactions among Iraqis and even within the committee" to softball.
"It's a game that comes from the United States and the Americans are seen as invaders," he said.
The 20 best female players have been invited to a training camp in the United States in July.
"My mother doesn't want me to go, but I hope she'll change her mind," said Jasim.
"It's the chance of a lifetime," she added.