1) Western liberal values are not co-extensive with Christianity. Christianity is geographically much larger. This has been true historically, and even more true today with the rise of Christian nations like South Korea and various nations in Southern Africa.
2) Western liberal values came to predominate in Europe centuries, even millennia, after Europe was Christianized.
3) Many Western liberal values are easily traced to pre-Christian movements, such as Greek Stoicism.
4) The Christianity of most Western Europeans today is not the Christianity of centuries ago, let alone millennia ago. The Protestant Revolution was like a giant flask where people took Christian doctrines and mixed them together with contemporary civil and philosophical values which emerged from the Enlightenment and then the dawn of the scientific and industrial ages. It's one thing to say that Christianity was conducive to the emergence of those other phenomena; it's quite another to say that they were Christian.
2) That's hardly a compelling case against the influence of religion on Western values. It could even be a contributor, or neutral.
3) These values were well-documented but, for whatever reason, did not spread to the Muslim or Hindu world first. Islam had its brief progressive renaissance but was not able to sustain liberal values over the long-term. There are some small exceptions - Ismaili Muslims are quite liberal - but they're a tiny fraction of the Islamic world.
4) America was essentially founded by religious zealots and/or adherents to marginalized religions. The very architecture of early America - the gothic styling of Boston, for example - is of that era and persists. You can't wipe out that kind of influence in 100 years.
I'm not saying religion is the ONLY factor, but I find it odd that people try to ignore the impact it's had on the shaping of the modern world. I'm an atheist so I view this more as a historical fact - I'm not a fan of organized religion and would be perfectly happy if it went away.
The Protestant Reformation was a religious movement, but ended up importing a lot of western beliefs into Christianity. Democracy for example is a western belief, Christianity is closely tied to Kings.
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I would argue that Christianity has influenced western culture far less than western culture has influenced Christianity. And that the key benefit attributable to Christianity—insofar as it was the lucky religion which happened be closest to the people who built western civilisation—is arguably its adaptable and relatively non-invasive nature compared to many of its contemporaries.
For example, Christianity is tolerant of the concept that God primarily operates indirectly through physical laws, a concept which was normatively rejected early in Islam (circa 1100). Thus, Christianity was relatively more conducive to the emergence of science. But, Christianity is hardly the only religion so tolerant, so it's not like it deserves special credit in that regard. Indeed, this tolerance is sort of a fluke and really a vestige of Roman and Greek influence--influence that Muslim scholars were deliberately rejecting.
Christmas trees and holly are obvious, but compare old vs new testament and it's much deeper than that. On top of that you get the Protestant Revolution which really westernized Christianity.