OTL that happened, it is called Salafism. People here have too positive a view of the Reformation, it was essentially a civil war, in Germany, that led to hundreds of thousands of deaths, for little positive.
The ideology behind “salafism,” from even a narrow point of view however, predates the fall of Baghdad. Ahmad Ibn Hanbal lived during the height of the Abbasid period and the Mihna (inquisition). There further is no such thing as a reformation in Islam and such a concept does not exist until Islam met the West in recent Ages. Islam itself constitutes a separate realm than that of those lands influenced mostly by Rome and the Church of the Middle Ages, just as it differentiates from Hindustan.
One thing should be noted, fiqh (law) and the interpretation of the classical masters of the Middle Ages was just as or more conservative than those scholars which followed them in the 14th century. This further is interesting considering the fact that no golden age disappeared. Egypt continued to improve itself following 1260 and great talent arose from there and surrounding areas. Post Mongol Islamic scholars were numerous and matched equally the skill of their predecessors. Ibn Taymiyyah for instance was prolific and is one of the most important scholars in the modern Islamic world. His works have been wholly preserved, kept and are still read. How many scholars of the 900s Abbasid period are still read today or do we have more than circumstancial evidences for their works? It is quite high. Whilst this may be evidence that the Mongol host destroyed it totally, the idea that everything known to the Abbasid was held in Baghdad, seems lacking.