What you have stated is the primary reason, the ethnic cleansing, the ethnic intolerance—and being Muslim did not help the Rohingya people, which is also a factor.
But I must assure you that if these Rohingya people did not happen to be Muslim—because of the Mughal empire's reach, they took their religion from it—they would have been Hindu. Or if the Christian missionaries went there, as they did in Karen state or in Kachin state, they would have been Christian. If these Rohingya were Christians or Hindus or any other religion, their genetic identity would remain the same, their race would remain the same.
If they were not Muslim and they were another religion, the Burmese would not have spared them. I assure you of that, because the anti-South Asian and anti-Indian sentiment is very high. This is a systemic issue. So that's why the Rohingya happen to be targeted at this point. We should remember that the people of the subcontinent, from India and Pakistan and Bangladesh, who went to Burma during the British time as business people were deported by the hundreds of thousands in the sixties.
So that sentiment has been there. But the Rohingya people are unlike folks from India, Pakistan, and Bangladesh who went to Burma during the British time for trade purposes, just as they went to Kenya and other countries. The Rohingya are an ethnic minority, an indigenous population that was living there before that. So after the Indians had left, the Rohingya became more of a target, because they think there is a remaining legacy of people of Indian culture, or South Asian I should say.