I would say that religion has provided order in the past, but no longer does so in many or most parts of the world.
Religion, like tyranny, is a mediocre ordering mechanism - it can take an absolutely chaotic system and bring a degree of order by making contrary behavior anathema and encouraging a certain set of communal cooperative activities. On the upside, this can bring cohesion to a community through homogonization and mutual participation; on the downside, this makes enemies of nonconformists and causes strife with them. The latter being a relevent issue the moment more than one religion comes on the block.
So, back in prehistoric times, religion was probably an ordering device - the societies were all going to be basically tyrannies anyway, and were all going to be attacking their neighbors at every opportunity anyway, so the tendency of religion to ostracize nonconformists wasn’t going to make the situation discernibly worse, which would its positive ordering effects as the only relevent effects.
Then, as time passed, religion became the vehicle for the creation of functioning legal systems - it might even be arguable that religion taught us how to have legal systems that were based on codified rules rather than, say, spontaneous edicts from the chieftan. (I couldn’t say for sure; IANAnAnthropologist.) In this regard religion would certainly be an ordering force…as it simultaneously taught us about a better ordering system than it, specifically organized civil government with codified legal systems.
As every modern nation has gradually drifted away from divine right of kings towards indisputably better government systems that have some form of democratic representation at their base, though, religion has been supplanted as the best system for maintaining order, and now rather than being most visible for its ordering aspects, it is now most visible for its divisive aspects. Rather than guiding us to make peace with our brothers (a role covered by cops now), religion now serves only as a font of war. Nobody could reasonably say that religion is a force for peace in the middle east right now. Or in europe. Or the states. In all these places, religion cannot make things better than civil law does, because even in the cases where it is having a cohesive effect it is redundant. The only notable effects it has in these places are the divisiveness and chaos it inspires.
So yeah. Religion is an excellent way to get from “REALLY chaotic” to “somewhat ordered”, but from there on up it resists global peace and order. It’s like a post with a bungee cord attached to it - while we’re beneath it’s natural level it pulls us up, but after that it pulls us back.
And regarding its effects on technology and science, I’d say it’s pretty clear that its effects on science are somewhat similar to its effects on order - religion gave us the knack for noticing things happening in nature and attributing it to consistent causes (any causes), and it brought us sufficient social order to be able to have monks sitting on their butts all day thinking and philosophising and possibly experimenting. But at that point you pass the post and religion starts pulling you back, figthing every discovery that appears not to support it or worse, to dispute it.