For one examination of this phenomena, I’d strongly recommend a book called The Rise of Islam and the Bengal Frontier, 1204-1760 by Richard M. Eaton ( 1993, University of California Press ).
In the case of east Bengal ( modern day Bangladesh ), his analysis appears to show that what you had in this distant border province, far from the center of the authority of the centralized Muslim states based at Delhi, was an area on the border of civilization, sparsely populated and incompletely penetrated by organized, formal brands of Hinduism. Attempts to convert the locals to Islam were actually discouraged by Mughal authorities for various reasons. Nonetheless, eastern Bengal was exposed to Islam and a process similar to ( but more complete than ) the syncretism described by UncleBeer took place - as Eaton describes it, in 3 phases:
a) Inclusion - “…the process by which Islamic superhuman agencies became accepted in local Bengali cosmologies alongside local divinities already embedded within.”
b) Identification - “…the process by which Islamic superhuman agencies ceased merely to coexist alongside Bengali agencies, but actually merged with them, as when the Arabic name Allah was used interchangeably with the Sanskrit Nrinjan.”
c) Displacement - “…the process by which names of Islamic superhuman agencies replaced those of other divinities in local cosmologies.”
At any rate for reasons to complex to go into more fully ( read the book
), Islam gradually became the entrenched folk religion of local woodcutters, farmers, etc. in eastern Bengal. Meanwhile Bengali hydrology underwent a major change beginning at least as early the 15th century, but greatly accelerating in the late 16th, where the Ganges shifted eastward, linking to the Padma system and profoundly altering access to the central portions of the Indian state in north India. The result was a slight decline in western Bengal, but an explosion in the no longer isolated and marginal east. The population boomed as land was cleared for agricultural expansion to connect to the now accessible markets to the west. In one smallish period, 1595-1659, revenue from northwestern Bengal declined by 13%, while revenue from the northeast jumped 97% and revenue from the southeast climbed even higher, up 117%.
This trend continued into the 18th century and was responsible for the phenomenal population growth of an area that had already accepted Islam, hence this seemingly somewhat anomalous large chunk of Muslim population sitting out there by itself, surrounded by mostly non-Muslim areas ( Arakan excepted ).