In a lecture I heard Srila Prabhupada say that our objective is not to compete with other religions, but rather to make everyone adopt Krishna consiousness. In what way can people adopt Krishna consciousness while being Muslims or Christians?

Prabhupada did not expect everyone to accept Krishna consciousness nor that other religions would come to an end. Rather, he wanted Krishna consciousness to become the light of the world.

Krishna explains in the Gita that faith develops in different persons according to their different modes of nature. Even in Vrindaban, which is preeminently Krishna’s land, we find some people worshiping other deities, though everyone knows and honors Krishna. Consider the great variety of religions in India, yet almost everyone honors Krishna. Over time, something like this will happen in other parts of the world.