Without Islam what religion Turkic speaking people hold ? Nestorian ? Buddhism ? Tengrism ?
will they will be easier to integrated to Mongol empire ? or will they still migrate to anatolia and iran ?
Turkic migrations preceded the expansion of Islam. Ghuzz Turks had began their incursions into Azerbaijan and the Oghuz were used as mercenaries by Heraclius at the battle of Nineveh in 627. It's notable that the Nestorian presence in Central Asia was largely caused by the Muslim conquests; uninterested in the Jizya and seeing Iraq become the center of the Caliphate they decided to expand their boundaries. Turkic speaking people would likely hold a variety of different religions. Mainchaeism was really the most popular, but Buddhism held importance among the Uighars. The Khazars would not convert to Judaism because there would be no need to such a thing in a political situation not split by two passionate religions, and Jewish refugees from Persia would not have come.
Their migrations are questionable. The collapse of the Gokturks meant that the various Turkic peoples were likely to be pushed in some direction; it is unsure which way. Some may spill along the Nomad super highway, but more may go into India with a fairly fluid route there occupied only by a few rulers only nominally tied to the Sassanid state.