How did Islam become the ideology of Pakistan?

Answer 1

It depends on how the question is read.

If the question is asking how Islam became the dominant religion in Pakistan, then: A Muslim army came through Pakistan on their way to India in medieval times. Islam was eagerly adopted by the people of Pakistan. Islam was the religion of many people in the Indian continent before the establishment of Pakistan and Bangladesh.

If the question is asking how the people of northwestern British Colonial India chose to create an Islamic state called Pakistan there, then: Muslims in Colonial India were afraid that a Hindu-majority India would persecute the Muslims in India. As result, they defined themselves by their Muslim-ness as a distinct group of people.