Sir Wilshaw refuted the claims when he was being questioned by a committee of MPs. The politicians said they'd received several complaints from parents, who said Ofsted was asking their children in appropriate questions and rating their schools unfairly.
Labour MP Alex Cunningham told Sir Wilshaw one parent claimed an Ofsted inspector asked her daughter if she was a virgin.
It comes as Durham Free School, a Christian school in north-east England, had its funding withdrawn from the Department of Education after Ofsted awarded it the worst rating possible. Durham Free School has said it will "fight" the decision.
Another Christian school in the north-east, Grindon Hall, was rated 'inadequate' and put into special measures. In this case, Ofsted said the school did not safeguard students properly, and failed to stop "prejudice-based bullying".
Mr Wilshaw said in response to claims Ofsted had an anti-Christian agenda: "Absolutely not. We're going into schools in Birmingham, Bradford, Luton, Tower Hamlets with children from predominantly Asian heritage, predominantly Muslim.
"We're failing those schools and putting them into special measures. We're saying tough things because they're not promoting British values, they're narrowing the curriculum.
"We're going to apply exactly those principles to all schools."
Speaking specifically about Durham Free School and Grindon Hall, Sir Wilshaw said: "These two schools are doing badly.
"Parents deserve better. Parents always try to support their school."
Graham Coyle, Christian Schools Trust, speaking to Premier's Marcus Jones on the 'News Hour':