Tolerance varied over time in the empire. Tolerance is also relative - Ottoman level tolerances where different religious groups are taxed differently and members of Christian families may be forcibly removed to be raised as Janissaries in some periods is not the same kind of tolerance that we imagine when we speak of tolerant societies today. The state did not implement a policy of large scale forced conversions, and Christians enjoyed property rights and protection by the state, however they were not "equal" under the law, nor was there any illusion that Islam was not the state religion. They would not tolerate public criticism of Islam. Only Muslims were permitted to testify in court against a Muslim. Apostasy was not tolerated.

I would not say that middle eastern states went backwards in terms of tolerance, rather it is more the case that they did not adopt the same kinds of attitudes at the same pace that European countries gradually did. Even today there are some countries in Europe whom have official state religions, or have laws against blasphemy on the books (even if not carried out in practice). It's also complicated because states in the ME vary between each other and over time. Turkey in the 20th century would be a lot more secular than Saudi Arabia would over the same time.

If you wanted to identify comparably recent trends moving towards or against secularity in the Middle East, I would point you towards Arab Nationalism and Wahhabism. Hopefully more learned members can go into further detail here, but in the 20th century ideas of Arab Nationalism took root in the fertile ideological soil of a colonial and post-colonial Middle East. The famous Egyptian statesman Gamal Abdel Nasser was one of many leaders of the middle 20th century espousing pan-national Arab ideologies, which included strong currents of secularism and a desire to modernise economically (often while walking a middle path between the Communist and Capitalist nations). At the height of their success, The United Arab Republic existed for a few short years as a political union of Egypt and Syria. This fell apart by 1961.

The secular aspects of this ideology were opposed by some, one of the most influential opposing voices at the time coming from the Wahhabists. These were people of a specific religious movement that is heavily associated with Saudi Arabia. They are conservative or possibly reactionary, and while Arab nationalism was discredited in the eyes of many after a series of setbacks in the 20th century, Wahhabism remains influential in some parts of the Middle East right up to the modern day.

Hopefully someone can drill a bit deeper there!