There is no supply of reliable historical evidence indicating that cultural and religious diversity contributed to the decline of the Ottoman Empire. From its earliest beginnings, the major cities of the Ottoman Empire were some of the most ethnically and religiously diverse cities in the world, centuries before multicultural cities, such as New York City, Chicago, Los Angeles, Toronto or Buenos Aires.
Cities, such as Constantinople itself/(the name , "Istanbul", does not come into existence until the 1920's), Thessaloniki, Izmir/(Smyrna), Cairo and Alexandria in Northern Egypt, had various ethnic and religious communities during Ottoman times. Turks, Greeks, Armenians, Jews, Egyptian Muslims and Christians had lived in these major Ottoman colonial cities for centuries and there was little disruption or internal disquiet that is historically documented during the early-middle years of the Ottoman Empire.
What contributed to the decline of the Ottoman Empire.......was the Ottoman Empire. From the failed 1683 siege on Vienna, into the early 19th century, the Ottoman Empire, was imploding. It was becoming an increasingly anachronistic imperial state that consisted of widespread corruption, as well as less than competent Sultans. It was also a part of the world that, despite its centuries long presence in Europe, was far from being European-(culturally speaking). In other words, the Ottoman Empire, during this above mentioned time, when compared with much of the European continent, was culturally and intellectually unsophisticated and at a long cultural distance.
These are the characteristics that may provide a solid foundation for better understanding the root causes and origins of the Ottoman Empire's 200 plus year internal decline.