This is a closed system. It's just our nature to be Humanists eventually and everything that gets us there is simply 'humanist values' or 'rational ethics'.
There is about as much chance of you accepting any Christian influence as there is of persuading a creationist that God didn't create the world.
Except it is not radically different, that the evidence shows the many of the core aspects of Humanism can be found in Christian theology. On the other hand, they cannot be found in Greek/Roman philosophy which Humanists tend to consider the major influence. Religion to them is simply a regression, a kind of error.
The process of change covers 2000 years (and before that there is another process of the evolution of ideas that led to Christianity). These ideas did not emerge fully formed, like all philosophies they evolve over time with diverse influences. They were not universally accepted either, ideas develop in radically different ways at the same time, and it is easy to find examples of completely contradictory stances in different Christian worldviews. Effects were not necessarily even intended, ideas take on a life of their own once released.
When we discussed this before you considered any mention of non-Christian society irrelevant though which makes the topic impossible to discuss.
Augustine of Hippo summarised Paul's theology as “Once for all, then, a short precept is given thee: Love, and do what thou wilt... let the root of love be within, of this root can nothing spring but what is good.”
I can't discuss the evolution of this idea without mentioning non-Christian societies so I won't bother.
Secularisation was often a violent and tyrannical process though as a result of 'rational ethics' being applied, why should it be considered a product of 'Humanist values'?
Ideas develop in numerous different directions, and this was equally true about things purportedly based on 'Enlightenment Values' that are supposedly the font of all goodness.
Tertullian, 2nd Century:
We worship the one God . . . There are others whom you regard as gods; we know them to be demons. Nevertheless, it is a basic human right that everyone should be free to worship according to his own con- victions. No one is either harmed or helped by another man’s religion. Religion must be practised freely, not by coercion; even animals for sac- ri ce must be offered with a willing heart. So even if you compel us to sacrifice, you will not be providing your gods with any worthwhile service. They will not want sacrifices from unwilling offerers – unless they are perverse, which God is not
The Greeks had democracy and it was
far from Humanist.
Reality premised on a particular worldview influenced by Christianity which they frequently acknowledged in their own words. There is no single 'source' of the scientific revolution, but numerous influences which influenced the cultural environment at the time. There are also some unintended consequences linked to Christianity (church translation of Greek philosophical texts, integration of these into theological education, the university system itself).
Newton on his natural philosophy:
You can compare this to 'irrelevant' non-Christian societies (China for example) to see why it is important and not just pure coincidence. The problem is that the modern Western worldview is so fundamentally ingrained in people's thought processes that the culturally conditioned is often mistaken for the natural.
Again, I can't discuss this meaningfully recourse to non-Christian societies.
Along with the idea that rights are bestowed on the individual and progressive history, the things you mentioned are pretty much the core concepts of Humanism though when combined with Greek rationalism.
Strangely enough, all are rare in historical societies and all are found in Christian theology. You see this as pure coincidence, and I don't believe ideologies give birth to themselves. So we get stuck.