Leather told a meeting of the Public Administration Select Committee last week that it was not in the commission's remit to make judgements about different faiths.
"It's perfectly within charitable law for religious organisations to have tenets of faith that not everyone in society agrees with," she said. "There's a tolerance of intolerance."
Leather said that this did not automatically mean religious charities were free to break the law. When they did, however, it was a matter for the police and not for the commission, she said.
Leather's remarks were delivered in response to questions by Gordon Prentice, Labour MP for Pendle in Lancashire, about the Finsbury Park mosque in north-east London.
Abu Hamza al-Masri, a cleric at the mosque, is serving a seven-year prison term for inciting murder and hatred. The mosque continues to enjoy charitable status.
Tony Wright, chairman of the committee, queried whether groups that propagate lies, such as holocaust deniers, should be able to access the benefits of charitable status. "Do charities have to say things that are true?" he asked.
Kenneth Dibble, executive director of legal and charity services at the commission, who also gave evidence, said: "We don't tend to enquire about the validity and truth of religions. That's not within our remit."
Paul Flynn, Labour MP for Newport West, said the commission's approach to religious charities was too light. "I get the impression that you're very tentative, very nervous about offending religious organisations," he said.
In April, the Department for Communities and Local Government gave the Charity Commission £1.2m towards setting up a faith unit that will try to combat extremism by improving leadership and governance in Muslim charities, including mosques (Third Sector, 5 April). A £1m grant had earlier come from the Treasury to help the regulator fight terrorism (Third Sector, 7 March).