> Put in other terms, the Western world in 2020 likes to act as if it reinvented itself afresh in the 1700-1800-1900s, but in reality, everything about "secular" knowledge has been formed in thousands of years of Christian culture
Both sides of that claim are fantastically false. First, while most describe the Enlightenment as novel, almost noone describes it arising ex nihilo rather than as a product of preexisting social forces, both building on and reacting against things present in its immediate context.
Second, while obviously it arose in a largely Christian context, there were significant non-Christian influences, and particularly the repopularization of pre-Christian influence (in part from interaction with contemporary non-Christian cultures) played a significant role in the Renaissance which itself set the stage for the Enlightenment.
> For example, the idea of universal human worth, human rights, and subsequently democracy (in the sense of every human being, not the Ancient Greek kind), is absolutely rooted in a Christian context.
Much of our idea of human rights is a reaction against the practices on all sides of the divides within Western Christendom.
> Had a different society had the industrial revolution first, things might be very different.
Sure, social evolution is path dependent. And if we adopted a cladistic taxonomy of belief systems, those stemming from the Enlightenment might usefully described as being subsets of "Christianity" because of their origin. But while cladistic taxonomy makes some sense for biological life, it really doesn't make sense for social movements.
> Or to ask a different question: if your values and actions indicate you as a group of X, but you vehemently deny (only with words) being a member of X, what does that mean?
It probably means that you and the people who think your "values and actions" make you part of X have radically different definitions of "X", and are essentially speaking different languages on that point.