Well the Sunni/Shia divide has been present in Islam since the death of Muhammad in 638 CE, Sufism was present, Ibadi was present as well. As for political divisions, well it depends on what you mean by Crusades. The Crusades period covered a span of time from 1092 to 1456 if you include every religiously based conflict between Christianity and Islam during the Middle Ages. But you could mean the numbered Crusades, which is what most people think of. They took place between 1096 to 1272. The amount of political divisions in both those spans of time in the Muslim world was staggering, for instance at the beginning of the First Crusade the Muslim world was divided between the Seljuqs, the Danishmends, the Fatimids, the Almoravids, and the Abbasids. These political divisions seen in the First Crusade would largely remain the same, along with the Ayyubids, Hafsids, and Bahri. The number of sultanates, empires, and assorted Islamic kingdoms in the Muslim world during this period in time were quite a lot. You may find THIS map helpful, despite it being largely after the contemporary Crusades(thanks to r/MapPorn).

I cannot type out a full answer for you right now but I highly recommend you read up on Saladin's life. I would pay particular attention to his life before the Third Crusade, as well as the beginning of the Third Crusade. I would also highly recommend the book Saladin by Anne-Marie Eddé. From these readings you should be able to see how Saladin acted as a unifying force for Islam during the period leading up to, and including, the Third Crusade. I would also just like to say that saying "around the time of the Crusades" technically makes your question span from 1095, with the beginning of the First Crusade, to 1492 which was the end of the Spanish Reconquista (which started in 718 but was considered a crusade after the First Crusade kicked off).