I fear that it's perhaps overly simplistic to say that Science would be far more advanced now in a world without religion. There are a number of reasons for this. Firstly, it's hard to say that a secular world would have done much to stop the Roman Empire from existing, advancing, and essentially dragging to a halt the advancement of Science and Mathematics in the Ancient Greek world (although even here it may have played its part, when the Roman Empire became Christian, so we might need to check the timing more carefully). Secondly, after this it was primarily the Christian Scholars in the West (and the Muslims in the Middle East) who were engaged in copying and preserving the knowledge of the Greeks, and while especially in the West it wasn't really taken any further, it might not have been preserved at all without this drive and need to copy it all down, again and again, preserving it for the future. How important or not the religious aspect was to all this is difficult to know, but it is true that most of the copying went in in monasteries or the equivalent.
Thirdly, it can be argued that the pursuit of knowledge for its own sake is a far less powerful motivation than the pursuit of knowledge through which you can know better the works of God. This was most powerful in the Islamic world, and indeed for a very long time the most advanced Science, Maths and Medicine went on there. Incidentally, this was also possible perhaps precisely because of the aggressive nature of early Islamic doctrine -- without such a powerful drive to conquer the world and bring enlightenment to others, would there ever have occurred the fusion of Indian and Greek Mathematics that was necessary to drive the subject forward to the heights it would achieve later?
This last is especially important, I think. Like so much else about this post, it's speculative at best, because we can't really know what the History of the world would have been without religion. It depends greatly on what would have replaced it. But it is certainly true that one of the most important events in the History of Science and Mathematics is the fusing together of the Geometry of Greece and the arithmetic-algebra of the Eastern world, and if this event had never happened, or happened much later, then Science would be many generations further back than it actually is.
It would be one of the world's greatest ironies if all the bloodshed of religious war had such a profound influence on driving Science forward.