There is a large community of Islam living peacefully in Myanmar. If you look around Yangon (the largest and most popular city of Myanmar), you could find a lot of mosques (some even closed to famous pagoda). So this issue is much more complicated than Islam vs Buddhism.
An interesting litmus test in situations like this is: are the Burmese Muslim population allowed to speak out about events around the Rohingya?
If, say, some Burmese Muslims held a large protest march in Yangon, would they run the risk of being targeted as a group? If so, I'd say that their silence is as a result of fear rather than support.
It's much more than religion. Of course, media would like to simplify things and only one side of the story would be told most of the time. But it's much more complicated issue in reality and the hatred is not one sided by the way.
