Saudi Arabia is undergoing a "huge transformation"

Saudi Arabia's religious conservatives believe women's sport is un-Islamic, and it's still banned in public schools.

But Lina Al-Maeena disagrees. In spite of many hardliners in her country considering her actions sinful, she founded a women's basketball club.

"I don't think it has anything to do with religion, I really think it's just out of chauvinism, out of male domination," she told CBS News' Holly Williams.

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In the last summer Olympics, when Saudi women competed for the first time, there were people on the Internet -- Saudis -- calling them prostitutes.

"We have been called names before," said Lina. "We've been labeled before. And it's very, I would say really sad to have people from the same country call each other that."

Saudi Arabia is an ultra-conservative, Islamic state. The male guardianship system means all women need a male relative's permission to work, or travel overseas.

For some, like Um Seif, a high school principal, those restrictions are not a problem.

Foreign women outside Saudi Arabia have more freedom than she and her countrywomen do, she told us. "But I don't want to be like them... From a young age we're taught that these are our customs, and we follow them."

But Saudi Arabia is changing.

Women now outnumber men at Saudi universities, and their government is encouraging them to join the workforce.

At Effat University, female students are planning careers in everything from engineering to filmmaking.

Dean Malak Talal Al-Nory told us her students have futures their mothers could only dream of.

"It has been a huge change, huge transformation, in almost every way," she told Williams. "It has been a change in the mentality, in the acceptance of women in the workplace."

The Saudi King is himself a reformer who's promoted women's rights.

But the King has to contend with religious conservatives -- whose support helps keep him in power.

The King is advised by the Shura Council, and he recently made 20 percent of its members women.

Some of those women told CBS News that any change has to be carefully managed, so the Islamic establishment doesn't fight back.

Asked if the pace of that change is frustrating, Shura Council member Thuraya Al-Arrayed laughed and said no.

"I'm a very understanding person. Change that happens overnight, that people aren't ready for, sometimes fires back ... backfires," she said.

Another council member, Dr. Thoraya Ahmed Obaid, is working on a proposal that would effectively end the male guardianship system.

"Men and women over 18 will be independent citizens of the Kingdom of Saudi Arabia. They will make decisions about their lives, that's according to this proposal for a family law," she said.

But all the women of the Council that CBS News met with said change has to come from within Saudi Arabia.

"I think it is our right to live the way we want to live without someone coming from anywhere in the world and saying, you're doing this wrong. It's nobody's right to say that," said Shura Council member Hoda Abdulrahman Al-Helaissi.