You have a point there. Up to a point, that is.
What you write is, by and large, the currently accepted mainstream narrative in Western culture. Two extremely important issues with this are frequently overlooked, though:
a) The scientifically advanced Islamic world of the early middle ages was the result of rapid military conquest of a sizeable chunk of places that were amongst the most advanced regions on the planet: the Hellenistic states, other left-overs from the Roman Empire, as well as various cultures on the Indian sub-continent. All these were conquered by force, and absorbed into the early Islamic states. And for some time, the new Muslim rulers presided over empires that were very technologically and scientifically advanced - because the regions they had conquered had already been very advanced before being absorbed into the new Islamic states.
And crucially, in the first few centuries, the ruling classes, and the clerics, did nothing much to impede the existing culture of science and letters in their new dominions - quite the contrary, they encouraged the spreading of technologies. Point in case: the "arabic numerals" you mention were brought to Europe from India by returning Arab conquerors. The scientific and cultural riches the Muslim rulers presided over were mostly not the product of Islamic culture per se, but they did not hinder the further development of what was there. And in some cases, considerable progress was actually made - there are a number of notable Muslim scholars from this era.
However, at some point, Islamic culture ossified (for reasons that are very complex, and not entirely understood even today), became increasingly hostile towards science, and created the backwards mess that we see today. It is crucial, though, to always bear in mind that the "golden age of Islamic culture" was never entirely a product of the Islamic world to begin with. Far from it, actually. Like everyone else, they heavily built on the foundations their predecessors had built.
b) The second point, that Europe only started to catch up once the influence of religion (read: Christianity) started to wane is simply not tenable, either. Not in a narrow reading, anyway. What happened from the Age of Enlightenment onwards was that the focus of society *and religion* changed in ways that made scientific endeavour possible and fruitful - crucially, without removing Christianity per se from public life, or the culture at large. Far too many scientists over time were Christian clerics for the narrow reading to be true: there are science-averse interpretations of Christian doctrine, but these are by no means exclusive, or dominant.