In my answer to another of the questions you have posted today, I noted that two of the three ways that Islam entered India (according to Bentley and Ziegler) were military ways. Arab armies entered Sind, in the northwestern part of India. A little farther east (and later in time), armies of people from Central Asia who spoke Turkish entered India as well. In both cases, Islam came into India via conquest. This is where India’s fragmented political situation comes into play.
Whenever a country is politically fragmented, it becomes more vulnerable to invasion. If a country is politically fragmented, its various regions might not trust one another and might not be willing to join together to fight invaders. The country’s regions might also have their resources depleted because they have been fighting one another. In either case, it will be easier for an outside power to invade the country in such a situation. This was what happened in India.
As an example of this, we can refer to Bentley and Ziegler’s discussion of Mahmud of Ghazni on p. 246 of the Brief Second Edition of Traditions & Encounters. There, the authors tell us that,
Taking advantage of infighting between local rulers, he (Mahmud) annexed several states in northwestern India and the Punjab.
From this, we can see that the fragmented political situation led to infighting that, in turn, allowed outside forces to invade successfully. Since these outside forces were Muslim, the fragmentation of India helped allow Islam to succeed in India.