Admittedly, I might be a little biased but I'd argue that religion hasn't stopped driving (or at least contributing significantly) to conflict, especially in the West. It may not be as explicit as it was in something like the Crusades, but it's certainly still there.

Like I've described before, antisemitism against Jews in WWII had everything to do with religious differences, although it manifested as racial hierarchy at the time; Jewish tradition interprets the laws laid out in the Torah (like in Exodus, Leviticus, and Deuteronomy) to mean that Jews should not charge interest on loans to other Jews while through the 19th century, many Christians believed that their scripture forbade charging interest on a loan. This difference is a significant contributor to the harmful stereotypes that fed into the antisemitic narrative that still rings almost a century later.

I've also argued recently that Leninism in the USSR resulted in something approximating a religious state through what was effectively mandated atheism. An interesting way I've seen the adjacent argument's phrasing is from Karl Popper's Conjecture and Refutations:

Theology, the Science of God, was replaced by the Science of Nature; God's laws by the laws of Nature; God's will and power by the will and the power of Nature (the natural forces); and later God's design and God's judgment by Natural Selection. Theological determinism was replaced by a naturalistic determinism; that is, God's omnipotence and omniscience were replaced by the omnipotence of Nature and the omniscience of Science.

Hegel and Marx replaced the goddess Nature in its turn by the goddess History. So we get laws of History; powers, forces, tendencies, designs, and plans, of History; and the omnipotence and omniscience of historical determinism. Sinners against God are replaced by 'criminals who vainly resist the march of History'; and we learn that not God but History (the History of 'Nations' or of 'Classes') will be our judge.

I understand Popper to say that even though many of the ideologies we've seen in conflict with each other may not appear quite like religions have typically presented, there is still an enormous amount of deification of those ideas which could be debated as an elevation to the status of religious belief.

Another similar example to the USSR is the struggle from the 60s to the 80s around the Catholic Church in South America were fueled by religious differences in some form or another. Left wing clergy members of the Church began using Marxist terminology which made it easy for the right wing extremists to accuse them of communist subversion; many steadfast supporters of the left wing movements (of those perceived to be) were murdered by various extremist groups, including Ignacio Ellacuría - who was murdered in 1989 alongside seven others in San Salvador - and Óscar Romero - who was shot while he was celebrating Mass in 1980.

I know that this might be something of a nebulous way to respond to your question, but I'm happy to discuss it further if you'd like!

References

Mysterium Liberationis edited by Ignacio Ellacuría and Jon Sobrino - the preface is a pretty powerful quasi-memorial to Ellacuría by Sobrino and it's definitely worth a read. There are also several very interesting essays included in this anthology.

Conjectures and Refutations by Karl Popper

No Salvation Outside the Poor by Jon Sobrino

And of course, Lenin, Stalin, and Hitler: The Age of Social Catastrophe by Robert Gellately - I feel like a lot of my responses include this book!