During an hour and a half appearance, she was repeatedly questioned by MPs over the inspection service’s policy towards faith institutions.
She said she had never been allied with “any secularist cause” and explained that remarks she had made in a recent speech about the need for “muscular liberalism” in schools were not about advocating secularism.
They were about “making sure we don’t inadvertently create spaces where intolerance can breed”, she said.
Mrs Spielman acknowledged some Orthodox Jewish schools had “a problem” with aspects of equality law.
According to independent school guidelines, schools must teach British values of respect and tolerance towards others, paying “regard” to groups protected under equality law - which include transgender people or those of same-sex orientation.
She told MPs she had been asked on occasions to “disapply” the law in this area when inspecting schools in order to respect parental wishes.
“This is a difficult one for Ofsted because we have no ability to selectively disapply the law in inspection. We have to work with the law as it stands,” she said.
Contrasting educational standards between independent and state schools, she said Muslim and Jewish state schools by and large performed “extremely well”.
The Ofsted head renewed her call for greater powers to scrutinise unregulated faith educational institutions (which include a number of yeshivot).