It is clear that they are not only asking for freedom of conscience - they are asking for consequence-free freedom of conscience, so that, in a jurisdiction where abortion or same-sex marriage are legal, Christians would be able to take jobs that involved carrying out or facilitating those things and refuse to do them, rendering their conscience superior to the law.
The obvious example is the registrar in Islington who thought she was being discriminated against when she was sacked for refusing to do the job for which she was being paid, viz. carrying out marriages and civil partnerships. The point here is that freedom of conscience is regularly treated as infinitely extensible once it is allowed as an exception - if you let Catholic doctors and nurses refuse to carry out abortions, they then move to redefining most methods of contraception as abortion, and refusing to carry them out either. There was a case not so long ago of a nurse who regarded her conscience as entitling her forcibly to remove coils from women she was treating on the grounds that to leave them in place would be to connive at abortion.
It is clear that they regard as part of that freedom of conscience the right to hate speech against LGBT people and discrimination against us in employment, housing and other areas. They regard us as intrinsically inferior and to be treated - compassionately of course - as such. Any attempt to oblige them to treat us as equal is claimed, explicitly, in this manifesto as an abridgement of their freedom of conscience.
In order to make these claims, they equate abortion and stem-cell research with genocide - the role of the churches in actual genocide in Rwanda and Bosnia ought to make them blush to do so - and equate same-sex marriage with patriarchal polygamy and incest. (They are on their best behaviour so they don't get into bestiality, and the record of various churches is such that they sensibly avoid paedophilia.)
What has this to do with the Transgender Day of Remembrance? Well, for one thing, one of the biggest rises in killings of trans women has come in Latin American countries dominated by the Catholic church but with a rising tide of Pentecostalist conversion - Brazil in particular. I am sure that police death squads are full of believers exercising their right of conscience. Many of the attacks on the provision of surgery and hormone therapy for trans people in the US have happened under the influence of the writings of Dr McHugh, a leading Catholic layman acting according to the dictates of his conscience. Catholic-run hospitals in the US increasingly regard treatment of trans people as being as out of the question as abortion or contraception. Demands that homeless trans people detransition as a condition of receiving social housing from faith-based groups are common, leaving vulnerable people in danger.
We hang together or we will be picked off one by one.
They say all this is done in the name of love - so were the burnings of heretics by the Spanish Inquisition, whose torturers and executioners sincerely believed that they were saving the souls of the Protestants, Jews and Muslims they murdered, and were acting, of course, in accordance with their consciences.
One of the reasons why I progressively detest the institution of organized religion as opposed to the simple faith of many actual believers is that endless talking about God and sacred scriptures and what they demand so often leads to mistreatment of actual human beings in the name of righteousness. Theology and religious law end up being blasphemies against the simple principles of love, kindness and justice which the religion of many believers is based on. (Some believers are just pieces of excrement walking around polluting the atmosphere, of course, but I am trying to be fair and not regard them as typical, any more than that well-known failed priest Joseph Stalin was typical of all non-believers.)
It's also notable how often believers end up telling lies or using half-truths when they are trying to justify immoral acts.
Perhaps we need to set religion aside for a while until we can practice common decency and abandon arrogant certainty about who is right and who is wrong.
*(The usual stuff - mentioning the Papal decrees against slavery but not the utter lack of enforcement of those decrees and the preparedness of the same Popes to receive financial support from monarchs profiting from the slave trade; mentioning the involvement of Evangelicals like Wilberforce in the abolition of the slave trade in the UK, but not the equally important role of freethinkers, and of Unitarians and Quakers whom many of those signing the current manifesto do not regard as Christians at all; mention of the role of Christians in the Civil Rights movement but not of atheists and Communists, and no mention of the role of other Christians in opposing it; mention of the Christian role in the fight against AIDs, but not of the wicked opposition of the Catholic church to condoms for prophylaxis and the mendacious claims of the American churches for abstinence-based policies. You know the drill.)