Why did religion mixed with politics hold back progress of Europeans but not the Turks?

Let's reexamine the wording of this question:

"Why did religion mixed with politics hold back the progress of the Europeans but not the Turks?"

This needs to be corrected in terms of historical geography and demography:

1. The Turks, were not on the world stage during the Middle Ages; that is to say, the burgeoning Ottoman Empire does not really emerge as a consequential Power until the 1300's-(at the very END of the Middle ages and shortly after the Crusaders left Constantinople after a 50 year occupation during the first half of the 1200's). So to associate the Turks with the Middle Ages, is just a historically erroneous. The Ottoman imperial heyday, was during the Modern Age...and NOT during the Middle Ages.

2. A better question might be asking, "Why did religion mixed with politics hold back the progress of the Europeans but not the Arabs-(or perhaps the Persians). The cultural achievements of the Moors and other Arab Muslims during much of the Middle Ages is well documented....especially in cities, such as, Toledo, Cordoba, Fes, Cairo and Baghdad-(but also in the cities of Uzbekistan in Central Asia).

3. There was never a separation of Mosque and State within Medieval Islam...in particular, Medieval Arab Islam. Religion, was very much, at the Center of daily life throughout the Medieval Islamic world and the laws that Muslims adhered to-(both civilians and elites), were religiously based laws. So to even imply that Arabian Islam or Persian Islam during the Middle Ages, was somehow, a quasi-forerunner to the 1st Amendment/(specifically, The Establishment Clause) in the U.S. Bill of Rights, is just an absurdity.

4. With regard to Christian Europe-(that is to say, Catholic Europe) during the Middle Ages, yes, throughout much of the Middle Ages, religion played a significant role in the lives of everyday people, so much so that it probably contributed to the stagnation and even the reversal of intellectual inquiry and creativity. One must remember though that during the Early Middle Ages-(500 AD/CE-1100 AD/ CE), the Greco-Roman literatures and texts were concentrated in a handful of Universities and Libraries far from the towns and small cities of Northern Europe. It was in the bigger cities, such as Constantinople, Baghdad, Cordoba, Toledo, Fes and Cairo where Classical learning (as well as the medical, mathematical and scientific advancements which accompanied it), was largely present. The Papacy-(which pretty much controlled most of the North European lands during the Early Middle Ages), did not necessarily "hold back progress" deliberately or purposefully; rather, it was an emphasis on piety and spirituality that was at the center of daily life. And such an emphasis on the outer worldly did not necessarily have to incorporate advancements in esoteric and scientific ideas......that would arrive in Northern Europe during the Late Middle Ages-(1100-1400/i.e. Thomas Aquinas).

5. There was one exception during the Early Middle Ages.......Charlemagne and the Carolingian Renaissance in Aachen, Germany. For a very short while-(during the second half of the 700's), Northern Europe did experience a mild cultural advancement under the rule of Charlemagne-(King of the Franks). Charlemagne did employ Artists, Architects, Musicians, Writers and Scholars within his Palatial Court at Aachen. However, the Carolingian Renaissance, was, short lived and did not have such a consequential impact on Early Medieval Northern Europe, though it did serve as an important forerunner and blueprint to the more scholarly based Late Middle Ages. When looking at Charlemagne's Carolingian Renaissance, one would not and should not accuse Charlemagne as deliberately "holding back progress".

So overall, the question needs to be seriously reexamined both chronologically, as well as ethnographically.

See here: Conflict thesis

The conflict thesis is the proposition that there is an intrinsic intellectual conflict between religion and science and that the relationship between religion and science inevitably leads to public hostility. Although the thesis, in its contemporary form, remains generally popular, the original form of the thesis is no longer widely supported among historians

Why did religion mixed with politics hold back progress of Europeans but not the Turks?

Religion didn't hold back European science (much), but something did. Something being the opposite of nothing. Nothing being zero.

The Arabs/etc had more advanced mathematics based on the number 0. This allowed them to work out all their other advances faster than the Europeans who were still saddled with Roman numerals. Maths is important for understanding scientific observations and discovering patterns, and sharing those discoveries with others.

Other things:

• Newer religion of Islam was less fractured/varied at that stage and required less suppression of heretical/competing beliefs like science was believed to be.
• They also fought fewer wars among themselves.
• Religion was decentralised unlike Catholicism.
• Had connections to India, China and scientific advances there.
• Access to Roman/Greek concepts and tech that weren't destroyed by barbarians.
• People in those times in colder places needed to spend more time on survival, less time to study. They do tend to make scientific advances related to survival needs though.

I appended the clause "but to a different degree" to your statement "The Ottomans' also had politics mixed with religion." And therein lies the heart of the issue.

The Ottomans were "somewhat," although not totally tolerant of other religions. That is to say that the degree of religious intolerance, and its related drag on progress was "much less" in the Ottoman Empire. For instance, "forced conversions" were frowned upon, at least officially (although they may have occurred unofficially).

On the other hand, parts of Europe were very intolerant. For instance, the Spanish Inquisition was mainly about forced conversions, and controlling the resulting "conversos." Not surprisingly, Spain suffered more than most European countries (after the end of the 16th century) from "lack of progress," even though she had been in the forefront earlier.

So to the extent that religious intolerance is a hindrance to progress, the effects of one on the other were far milder in the Ottoman Empire than in Europe.

I do not know what measure you use to determine technological advancedness, but it to speak about Italy, it was much more scientifically advanced than the Muslims up until renaissance when other European power such as France, England and Germany catched up.

Just count the number of books published in Italy in in the Muslim world so to get rid of any illusions: this number was much higher for Italy even before printing press was invented.

You are badly confusing rate of progress with state of knowledge. Yes, the Turks in the Middle Ages had greater technological prowess than Europeans, but they were already woefully under-achieving in terms of progress. The origins for this state of affairs lies in the different progressions of collapse of the Roman Empire in the West and the East.

In the West, numerous diverse tribes overran the Western Roman Empire in the fifth century CE and promptly set to squabbling over the spoils amongst themselves. At this same time (possibly in consequence) there was also an agricultural collapse in the West that for a few hundred years delayed the restoration of a middle class with the leisure time to pursue scientific research and engineering development.

By the time of Charlemagne in the 8th century the [monastic and cathedral schools that evolve into] universities are being established across Western Europe, and the underpinnings of the Renaissance are being laid. Bell-making is being perfected, which will provide great returns when the (comparatively) simpler metallurgy of cannon-making must be mastered. Rapid advances in iron-working are sowing the seeds of knowledge that will allow iron as well as bronze cannons to be cast reliably, and the development of iron-barrelled firearms. Double-entry bookkeeping is developed, allowing the formation and management of share-equity corporations to finance exploration as well as scientific development and insurance. Although starting from a much retarded base, by the early middle ages scientific and engineering progress in Western Europe is already out-stripping what is occurring in the Middle East, rapidly incorporating and expanding on all Eastern ideas that are encountered.

In contrast, the wave of Muslim conquest in the 7th ad 8th centuries that dismantled all of the Eastern Roman Empire (except Anatolia and the Balkans) was not followed by an agricultural collapse. The middle class continued in existence in its conquered countries, carrying forward the accumulated knowledge of Roman, Greek and Parthian civilization. However, from a starting point a few hundred years in advance of Western Europe, in barely as many years the Muslim world stifles all research and finds itself a scientific backwater, with the Ottoman Empire rapidly being identified as the sick man of Europe from its total incompetence in governance, science, engineering and military capability. By this time, in the 15th and 16th centuries and extending to the modern day, it is the Muslim world of the Middle East that is seemingly incapable of incorporating any Western ideas and technologies into its culture.

Rebuttals:

• Al Khwarizmi dies about 850 CE and Al Hazen dies about 1040 CE. University of Bologna is teaching students starting in 1088, and Oxford is teaching students by 1096. If the strongest argument against my case is that the highpoint of Islamic intellectual achievement was over 900 years ago, I rest my case.

• While universities as government chartered institutions granting advanced degrees only rise about the midpoint of this timeline, the cathedral and monastic schools from which they arise, as centres of learning where academics and scholars gathered to teach, debate, and advance their own learning are much older.

• From The Origin of Universities (my emphasis):

  Note that because the awarding of academic degrees for advanced studies was historically a European custom, and the modern definition of a university includes the ability to grant degrees, the oldest institutions of higher learning that have always satisfied the modern definition of a university were in Europe. If, however, the definition is broadened to include ancient institutions that did not originally grant degrees but now do, then some European and non-European institutes predate the University of Bologna (for example, Nalanda University had been established by the 5th century BC in India [now in ruins], Nanjing University founded in 258 in China, and Al-Azhar University founded in 988 in Egypt).

  Because of the above definition, there is some controversy regarding what is the world's oldest university. If we consider university simply as a higher education institution, then the choice is between Takshashila, Nalanda and Al-Azhar University, but if we consider the original meaning of the word (from the latin "universitas": a corporation of students), then universities would be a medieval European phenomenon with the oldest university being the University of Magnaura in Constantinople (now Istanbul, Turkey), founded in 849 by the regent Bardas of emperor Michael III.

• The phrase sick man of Europe may be a 19th century one, but the sentiment and thought was not. The ability of the Ottoman empire to positively influence its own destiny was in rapid decline following Ahmed I's reforms of 1603 to 1617.

• At least one Florentine banker is known to have been using double-entry bookkeeping by 1211. The absence of proof of earlier use is not proof of absence of use. As a significant competitive advantage, by way of making embezzlement more difficult for starters, there was every reason for users to keep this knowledge proprietary as long as possible.

• Let's take the Middle Ages to be the millennium from the fall of Rome in fifth century CE to the fall of Constantinople in 1453. By 670 Western Europe is an intellectual backwater in consequence of the agricultural collapse of 200 years earlier, while The Eastern Roman Empire is at its political and intellectual zenith. By 770 the Islamic conquest of the Middle East, North Africa and Spain has moved the intellectual centre of the East to Spain, Egypt and Iraq, and Islamic intellectual capital is probably 300 years ahead of Western Europe. By 1100 when the First Crusade conquers Palestine, one cannot but argue that the two cultures, whilst exhibiting different strengths and weaknesses, are roughly equal in capability and intellectual capital. The East has all but stood still for three hundred years while Western Europe advanced.