It's a complicated conflict. It's chic to blame the military junta for everything, but the vast majority of Myanmar people support the military's action against the Rohingya. Tragic but true. Generally I am of the opinion that people who live in a place tend to know their own politics better: I assume there are reasons, unknown to or ignored by the international media, why the conflict has boiled over to such an extreme level.
It's the same reason why I'm willing to listen to Americans who support Trump, even if he seems crazy to me (and most non-Americans).
Kstat is also right to point out that it's not unlike a border conflict between Bangaldesh and Myanmar. "Rohingya" is an invented name for Bangladeshi-descent people brought into Myanmar during British colonial times. They were neither native nor accepted by the native people. I think religion is only part of the story: it is combined with ethnicity and nationality divisions too.
Another related factoid about Muslims vs non-Muslims: in China, there are 2 ethnic groups which are predominantly Muslim (Hui and Uighur). The Hui look ethnically similar to the majority, but the Uighur look different, and have separatist political intentions. The Hui live more or less peacefully with the majority, and are free to practise their religion to their hearts' content. It's never really entirely about religion: it's a mixture of factors.