Let us take for example the standard account of Arabs in Spain, Turks in parts of the Byzantine Empire, or Arabs and Byzantines. You would see it from the geopolitics standpoint, as a tug of war. Yes, there is a tug or war, but not in the sense that you suspect. Merchants were doing business very actively during that period. My own existence as Greek-Orthodox of Byzantine rite living under Islam is witness to such collaboration.
Peace: Neither Ink nor Blood
Nassim Nicholas Taleb

Excellent point. Türkmen tribes were footling around Anatolia well before the battle of Manizkert, generally just grazing their sheep and doing business.