Christian Concern claimed that the new charter, released on Friday, goes against the Church's beliefs and Bible teaching.
Chief executive of the charity, Andrea Williams, said in a statement: "The Church of England has a God-given opportunity and responsibility to set the culture of its schools in line with the teaching of God found in the Bible. But instead, it consistently capitulates to the spirit of the age as, for example, expressed in statute by the Equality Act.
"This charter fails to protect teachers, governors and children who wish to state and uphold the Church's own teaching on marriage and family.
"It also represents a missed opportunity to bring the good news of God's purposes and pattern for human relationships to the confused and toxic environment in which the one million children they are responsible for are having to grow up."
Williams also said that the Church contradicted itself in the charter when it quoted scriptures.
"Bizarrely, the document starts by selectively quoting two verses of scripture that would radically undermine the position it goes on to state," she said.
"Genesis 1:27 is first quoted: 'So God created humankind in his image, in the image of God he created them' but the document omits 'male and female he created them' - a truth at the heart of the transgender debate raging in our schools and society.
"Then John 10:10 is quoted: 'I have come in order that you might have life—life in all its fullness' without citing the first half of the verse: 'The thief comes only in order to steal, kill, and destroy.' This refers to teachers who lead God's people away from the truth."
"In this exact parable, Jesus' message is abundantly clear: there is only one truth, to be found in him. His warning is stark to a church that would lead little ones astray - even using language of death and destruction.
"Surely it should not be difficult for the Church to boldly stand with Jesus and his teaching that is stark yet loving, liberating and life-giving. This is the firm foundation on which all education in our nation was once built."
The Church of England's guide comes at a time of major debate over relationships and sex education in England's schools, with the subject due to become a legal requirement next September.
The new charter has eight commitments which all schools, Church of England and others, can sign-up to prior to the new guidelines becoming law.
The charter says that CofE schools should ensure that the curriculum "protects, informs and nurtures all pupils" and clearly differentiates between factual teaching on topics such as biology, the law, marriage and different types of families and moral teaching about relationships and values.
Derek Holloway from the Church of England's Education Department told Premier on Friday that an important part of the guide is delivering the curriculum in a faith -sensitive way.
"It's key that it's going to be delivered in a way that affords dignity and shows respect to all the groups that make up our diverse community. We have as a principle at the bottom of this, the idea of faith-sensitive and inclusive RSE, which means taking into account the views of the communities, including the faith communities that are served."
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