The Christian Institute said in a statement that the Government inspectorate has an "obsession with forcing primary school children to learn about same-sex relationships".
The criticism comes as the head of Ofsted, Amanda Spielman defended school lessons on same-sex relationships.
Speaking to the BBC, Spielman said the lessons were "about making sure they [children] know just enough to know that some people prefer not to get married to somebody of the opposite sex and that sometimes there are families that have two mummies or two daddies".
She added: "It's about making sure that children who do happen to realise that they themselves may not fit a conventional pattern know that they're not bad or ill."
Both Christian and Muslim parents have raised concerns that the lessons are not age-appropriate and undermine their religious beliefs that hold marriage is a lifelong union between a male and female.
Colin Hart, director of The Christian Institute, said: "Amanda Spielman's remarks today are not going to help.
"It's LGBT issues that we always seem to be hearing about. Parents want Ofsted to ensure the quality of education. They don't want Ofsted side-tracked into identity politics.
"The fact that same-sex marriage exists is something that can be covered in secondary schools. Not every controversial issue has to be covered in primary schools."
Mr Hart concluded: "The idea of teaching ever more detail about sex to ever younger children is deeply worrying. Treating parents who object as homophobes is not the answer.
"They just want to protect their child's innocence. Ofsted have some work to do in restoring the trust of parents who have a religious faith."
"Parents read the papers. They've seen the furore over Ofsted inspections at Jewish and Christian schools. Now Muslim parents in Birmingham are concerned about the level of LGBT teaching in their primary schools.
"Instead of listening to parents or allaying their concerns, the Chief Inspector of Schools seems to be casting doubts on their integrity. Implying that parents' desire to protect their own children is from fear, ignorance or possibly even homophobia."
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