I don't know that the rise of secularism had anything to do with Christianity.
Whatever peaceful message Jesus Christ preached, it still failed to prevent Christians from carrying out the most savage of atrocities on each other (and also on persons of other religions, including Jews and Muslims). I know that different things frighten different people, but to me, burning people to death at the stake is an even more cruel way of killing them than stoning or beheading. Both Catholic inquisitions and Protestant reformers were guilty of carrying out this "cruel and unusual" form of punishment - and all in the name of the "Prince of Peace", Jesus Christ!
In 19th Century New Zealand, it took the newly-converted Maori people very little time to wake up to these facts. They quickly noted that the Ten Commandments took a distant second place between Monday morning and midnight Saturday - then got placed on indefinite Leave of Absence whenever there was a war on!
Similarly, the same point was not lost on African people. So much so that they developed a parody of the hymn "Onward Christian Soldiers", which reads:
Onward Christian soldiers, into heathen lands,
Prayer books in your pockets, rifles in your hands.
Bring the happy tidings, of where trade might be done,
Preach your Peaceful Gospel, with the Maxim gun.
(Those familiar with firearms will know that the Maxim was the world's first automatically-firing machine gun. During the late 18th and early 20th Centuries, it was the Weapon of Mass Destruction. European colonial powers made widespread use of it to "pacify" the "savages" of Asia and Africa). )
As all of us here should be aware (being former JWs), people can read the bible until they are figuratively "blue in the face", it still does not necessarily turn them into better people. Our enlightened Western society is definitely the product of Secularism, not of reading the bible.
Whether or not Secularism is the natural result of Christianity, though, is quite another matter. It could possibly be argued that Secularism gradually evolved in response to such disasters as the Thirty Years War (1618 - 1648), or the Spanish Inquisitions; with a view to keeping all future religious disputes to the verbal level? If so, it largely succeeded - whereas Jesus Christ's "Gospel of Peace" had very little effect on matters!