I really do not know what you mean when you say Muhammad's armies destroyed Greco-Roman civilization because Muslim conquest of Byzantine happened after his death. Muhammad never fought any majjor war against Christianity. His military career was mostly against his own tribe and they were pagan Arabs and in that he was assisted by Christians. Islam's first alliance was with Africa's Christian King Najashi who regarded Koran to be a miracle from God!
One thing you must know about Hagia Sophia's conqueror is that he (Mehmed 2) was actually adopted and raised by a Christian Queen whom he regarded as his mother. Ottoman Sultans had a long tradition of marrying Christian women from European nobility. If we were to make a list of every single Ottoman Queen that ever lived, we will see that some of the most powerful Ottoman queens who ruled over important provinces and even led negotiations on behalf of the Ottoman Empire were in fact Christian. There is a very long list but the three notable Christian queens of the Ottoman empire that we can mention are as follows:
Theodora Khatoon, a Byzantine Princess who married Sultan Urhan in 1346. She was active in supporting the Christians living under Ottoman rule and built a lot of Churches. In 1347 she gave birth to her only son, Şhahzade Halil, who married Princess Irene, the daughter of John V Palaiologos.
Tamara Khatoon, born Kera Temara (Bulgarian: Кера Тамара
was the daughter of the Bulgarian Emperor Ivan Alexander and his second wife Sarah-Theodora. Tamara was a sister of Ivan Shishman and Ivan Sratsimir. She was born in the 1340s and originates from the Shishman dynasty.
Despina Khatoon, born Mileva Olivera Lazarević, (Serbian Cyrillic: Деспина Оливера Лазаревић; 1372 – after 1444) was the youngest daughter of Lazar of Serbia and Princess Milica and the wife of Ottoman Sultan Bayezid I. After the marriage, she became Despina Hatun (Turkish for "Lady Despina").
Most of the Christian Queens of Ottoman empire followed Orthodox Christianity but some were devoutly Catholic. This meant that the Ottoman courts always hosted rivalries between Sultan’s Catholic wives and Orthodox wives. Catholic queens communicated directly with the Pope and pushed for a foreign policy that would favor the Catholic world. Orthodox queens maintained similar relations with Orthodox Church and were always pushing for an agenda that would favor Russia over Catholic Europe. In both cases they often raised Ottoman Princes and Princesses who were devout Christians. This actually helped the Ottomans because the Christian world did not want to be ruled by Muslims directly. By having Christian children in their families Ottomans were able to place their own Christian family members in important positions in Europe.
The Ottoman Sultan Mehmed (2) who conquered Constantinople is a very well-known historical figure. Yet what most people do not know about him is the fact that he was raised by his step-mother who was an Orthodox Christian queen by the name of Sultana Maria Brankovic or Sultana Mara. She was the daughter of Serbian monarch Đurađ (George) Branković and Eirene Kantakouzene. She married the father of Mehmed II, Sultan Murad II. You will notice that this woman does not carry the usual title of Khatoon (lady) after her last name. She directly entered the Ottoman court as “Emerissa” (Higher queen) and then became “Sultana” (the grand Queen.) In the history of Ottoman Queens very few women ever rose to the ranks of Sultana’s and Maria Brankovic was one of them.
Ottomans were allowed four wives at the same time. Unlike European monarchic order, the rank of a Queen in Ottoman empire came in three categories. Most queens were “Khatoons” who were given provinces as dowry. They held powers of provincial administrators and collected revenue from those provinces. Very few rose to the second rank of Emirissa. This is when the Queen would have influence outside her assigned provinces, would also have battle units and could influence the foreign policy of Ottoman Empire. Final rank was Sultana who would have her own flag, her army and many provinces. She would have most powers of the Sultan on a lesser level. Maria Brankovic came into the court as an Emirissa and became Sultana after a very short time. All her life she campaigned for her favorite stepson Mehmed II to become the next Sultan and after the death of her husband, Mehmed did go on to assume the throne. Right after becoming Sultan he assigned Maria Brankovic as his official advisor.
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During Sultan Mehmed’s time Maria Brankovic was addressed as Valide Sultan (Queen mother.) Her powers grew to the point where members of the Orthodox Church in Russia could not appoint its members until they were approved by her. She also began negotiating foreign agreements on behalf of the Ottomans and represented the Ottoman empire during the negotiation of the Ottoman-Venetian war. [/FONT]
In the end, just like you can not hold Christianity responsible for American foreign policy, Ottoman politics are also far too complicated to be reduced to a simplistic "ISLAM VS CHRISTIANITY" affair.