Christian Concern is urging the government to protect the free speech of teachers who do not agree with using transgender children's preferred gender or pronouns.
The government is due to publish new transgender guidance for schools but has refused to say whether teachers can refer to pupils by their legal and biological gender in a written answer to a question put by Lord Pearson of Rannoch.
Lord Rannoch asked for clarification after the Teaching Regulation Authority (TRA) banned Joshua Sutcliffe, a Christian, from teaching indefinitely for allegedly 'misgendering' a pupil.
Answering on behalf of the government, Baroness Barran, Parliamentary Under-Secretary of State for Education, declined to say whether teachers like Mr Sutcliffe would be protected.
She said, "The department recognises that gender is a complex and sensitive issue, and that some schools and colleges feel that they need more support in this area in order to help pupils, students and parents deal with concerns raised.
"That is why the department is working with the Minister for Women and Equalities to develop guidance to support schools and colleges in relation to gender questioning children.
"The department has committed to publishing a draft for consultation at the earliest opportunity."
Andrea Williams, head of Christian Concern and the Christian Legal Centre, which has supported Mr Sutcliffe in his case, said the response was "shocking".
She called on the government to issue guidance that supports teachers who refuse to use language that does not align with pupils' legal and biological gender.
"No teacher should face disciplinary sanctions for speaking the truth about who a pupil is in law and biology," she said.
"Contrary to what the government said, legal and biological gender is not complex. Boys are boys, and girls are girls. The government is wrong to claim this is complex. No previous society has found it complicated."
She added, "The fact is that school pupils cannot change their legal or biological gender. The government should make clear that pupils are not allowed to socially transition and teachers should refer to pupils by their legal and biological gender."
