Christian Concern is supporting calls for a public inquiry into Stonewall's influence in UK institutions after an exodus of organisations from its diversity programme.
Stonewall advises over 850 major employers in the UK, including many government departments, universities, police forces and schools, covering a quarter of the UK workforce.
But equalities minister Liz Truss has urged all government departments to leave Stonewall's Diversity Champions Scheme.
The Ministry of Justice announced this week it was withdrawing because of concerns over free speech and Stonewall's "dubious" training.
The Equalities and Human Rights Commission, and Ofsted have both walked away. Further afield, Channel 4 has left it too.
Christians have long been concerned about Stonewall, but feminist voices have increasingly challenged the LGBT group's influence because of its stance on transgenderism.
It was recently reported that Stonewall was advising organisations to replace the term 'mother' with "parent who has given birth" as a way of boosting their ranking on its inclusive employers league table.
The campaign group Sex-Matters is demanding a public inquiry, a call backed by Christian Concern.
In her letter, Christian Concern chief executive Andrea Williams said it was "beyond question" that Stonewall's influence had been "damaging for standards in public life".
"If holders of public office are accountable to the public, then this is no longer evident in many institutions given the vast influence that LGBT organisations and ideology now hold over them," she wrote.
"Government responses to public participation in its consultations on matters such as on same-sex marriage and Relationships and Sex-Education, show that principled public opposition is disregarded."
Commenting on the letter, Williams said the "extraordinary" exodus from Stonewall's diversity scheme showed that many institutions were waking up to the threat to free speech and religious liberty.
"Organisations and bodies at the highest levels are beginning to see the extent to which Stonewall has captured their institutions and the lengths they are prepared to go to go to silence religious beliefs, freedom of speech and any criticism of its ideology," she said.
"Yet this exodus has only scratched the surface of the hold Stonewall has on so much of our public life.
"Too many Christians have been faced with the choice of standing by their beliefs or losing their jobs because of the grip of Stonewall's ever expanding LGBT ideology has in the workplace.
"We call on Lord Evans to look closely at the evidence and for a full public inquiry."