It's not just about Islam, the entire Arab world. How did they went from being ahead of the rest to being the latecomers?

From the 8th Century to the 12th Century AD, the Arabian Muslims were more advanced in critical reasoning and quest for truth. Even Christianity rediscovered critical reasoning from the Arab world.
During this time, nobody was killed in the Arab world for not believing in Mohammed or in interpreting the Koran to his taste. The worst that was done to people who interpreted the Koran differently was excluding them from the general Muslim assembly while according them the right to establish their own sect.

Today, I wonder if a Muslim can interpret the Koran to his own taste without being charged of blasphemy or without being killed.

That's like asking what happened to the Roman Empire, or the Aztec Empire or the Songhai Empire or the British and so on and so on.

They simply wax and wane and evolve, which is why Islam that was limited to the Arab world has now spread all over the world, just as British English has and Roman law too along with ideas from Songhai and Azteca, each solving the problems of their time in their place.

While you see regression in some individuals you might be looking at, some see progression on the larger scale of society.