Actually most of the Turks choosed to fight against Muslim Arabs at the beginning. Khazars were between Arabian and Byzantine pressure, so they simply choosed Judaism, which is recognized by both religions. Kypchaks (ancestors of Kazaks), Oghuzs (ancestors of the Turkey, Azerbaijan and Turkmenistan) and most of the others tried to stay as Tengriists while the Uighurs (modern day inhabitants of Xinjiang) choosed to be Manicheans.
Some Turkic people, like Volga Bulgarians, choosed to be Muslim because of political support of Abbasid Caliphate against Kievan Rus and other Tengriist Turkic people. But there're so many Arabian sources which claim that this conversion was not sincere. In Arabian sources, Turkic picture was all about raiding, drunken barbarians who never wash themselves (because of religious reasons); or a people who wants to use Caliph's economical power. Ibn Fadlan says that Bashkir Turks worship fallus idols because they believe that they're alive for only this and they know no other god.
How the Islam spread so widely among Turkic people? There're 3 major events.
1- Battle Of Talas: Muslims launched an attack to Transoxiana (modern day Turkmenistan and Uzbekistan) and Chinese responded this attack by making massacres in Turkic cities which didn't try to stop this invasion. After this massacre, a huge force of Karluk Turks changed sides and joined Muslims. Chinese lost the battle and Karluks choosed to convert Islam after an agreement about their autonomy. They founded a state, named Karahanlı and became a major power in Central Asia.
2- Seljuk Bey: As a son of a rebellious vassal of Oghuz Yabgu, Seljuk gathered his tribe and conquered the city of Jand in Persia. Oghuzs were Tengriist at that times. He choosed to become muslim so he had no obligation to pay taxes to heathens (his former sovereign lord). Because of the regions instability and his military successes, more and more Turks started to join him. Eventually his grandsons became the swords of the faith, defeated the Byzantines and started to settle Persia, Syria and Anatolia. Althought they're muslims, there're jokes about their early khans in Arabian world. They're militarily superior but their intellectual level was not enough for Abbasid times. Still one of them (Tughrul Bey) managed to marry with one of Caliph's daughter.
3- Mongol Invasion: Mongols, as distant cousins of Turks, were using the old steppe warfare methods which was very familiar to the Turks. But at those times Turkic states in Persia were highly Persianized and their military style was different from two centuries back. So when the Mongolian conquest began, another Turkic wave came from Central Asia and joined their kinsmen in Syria and Anatolia. Anatolia was, like always, a craddle of all kinds of beliefs and races. Muslim scholars like Rumi were preaching peace and unity, Turkic Muslims were not far away from their Tengriist roots; so they tried to find a synthesis between Old Ways and Islam. That's why the modern day Turks are, I believe, the most moderate muslims. There're still Tengriist or Shamanist practices which they use in their daily routine. After this mass migration, Anatolia highly populated by Turks and eventually became muslim. Still there were heterodox religious movements, but all of these movements were using the name of Islam.