The Christian Institute is threatening legal action against Warwickshire County Council over its "deeply flawed" Relationship and Sex Education (RSE) policy for schools.
The policy asserts that gender identity "can be best understood as being a spectrum" and "transgender children have the right to use whichever toilet or changing room they feel most comfortable using".
In addition, the policy suggests that schools do not need to inform parents if their child is transgender or if a child is using school facilities according to their chosen gender.
Controversially, it incorporates the All About Me programme that teaches primary-age children about sexual development, including masturbation.
Guidance for Year Two - children aged as young as six - says that: "Children will consider their own rules for how they like to be touched by others and the rules of when it is appropriate to touch themselves - including self-stimulation."
The council is currently reviewing the programme after Rugby Conservative MP Mark Pawsey raised concerns that the material was not age appropriate. However, All About Me remains listed on a number of local school websites.
Lawyers acting on behalf of The Christian Institute have written to the council citing a "catalogue of errors" in its approach to RSE.
The organisation said that the council has failed to "take into account and give proper weight" to its duties under the Equality Act 2010, the Human Rights Act 1998 and the Education Act 1996.
Elsewhere, it raises concerns over safeguarding and the protection of single-sex spaces.
"The Policy has had no regard to the fact that the Equality Act includes several exceptions, for example, in relation to discrimination on grounds of sex and gender reassignment in the provision of single or separate sex services (see paragraphs 26, 27 and 28 of schedule 3 to the Equality Act)," The Christian Institute states.
"In each case, the restriction must be objectively justified. However, the lack of any reference in the Policy to such exceptions will mislead teachers and schools into acting as if equality law confers absolute rights on transgender children and they will fail to take account of the impact on other pupils.
"The Policy also states that transgender children have the right to decide who knows they are transgender, when they tell people and how to tell people. But concealing information about a child's transgender status could give rise to significant safeguarding and privacy breaches."
John Denning, The Christian Institute's Education Officer, said: "The Council must withdraw this deeply flawed policy while it addresses its catalogue of errors."
The Christian Institute has asked Warwickshire County Council to withdraw the policy and write to local schools "to make clear to them that their continued adoption of the policy could lead to them breaching the legal obligations".
The council later told The Christian Institute that it did "not intend to provide a substantive response" to its legal and policy arguments, and that it is undertaking an "independent review" of the programme.
It also refused to make any promise about withdrawing the policy.
Mr Denning accused the council of being "reluctant to engage" with parents or The Christian Institute over their concerns about the policy.
"The Council is utterly failing to balance the rights of trans-pupils with the rights of others," he said.
"At the same time, it has commissioned materials for use with small children that are highly inappropriate, radically ideological, yet inexplicably, completely silent on marriage."
He added: "The Council must withdraw this deeply flawed policy while it addresses its catalogue of errors.
"As it does so it must rid itself of the notion that young children somehow want or need adult ideas forced upon them or that it is both legal and desirable to keep their parents in the dark about it.
"There are vital safeguarding issues at stake here. To refuse to admit there is anything wrong with the policy would seem to be putting at risk the well-being of the very children they have a duty to protect."
Responding to the claims and threat of legal action, a Warwickshire County Council spokesperson said told Christian Today: "It is not our policy to comment on matters that are subject to potential legal proceedings."