Myanmar has been doing an ethnic and religious cleansing for years, possibly more than a decade. The regime wants an all-Burmese, all Buddhist population. There are multiple refugee camps near the Myanmar border in neighboring Thailand.
As implied above, the US MSM have been largely ignoring Myanmar's ethnic and religious cleansing for many years. My cynical - though possibly at least partly correct - thought is that one of the first ethnic minorities affected was the Karens, who are largely Christian. The MSM don't like reporting persecutions and killings of Christians (e.g. the unreported 2-decades-long ethnic and religious cleansing the Arabic government of Sudan carried out against the black Christian and Animist south (that became the nation of South Sudan). This is the first I've heard of Myanmar persecuting Muslims, though I knew it was likely to happen.
India has had conflicts with neighboring, Muslim, Pakistan since before the were divided by the Brits and became nations. There has been a lot of Muslim-on-Hindu and Hindu-on-Muslim violence, much of it organized. then there's the terror attack against that hotel in Mumbai, several years ago, which originated in Pakistan. I suspect that India looks on these Muslim refugees as a potentially very large container of annelids.
Bangladesh borders Myanmar. I don't know whether they have taken in any refugees, but they aren't exactly a rich nation with plenteous jobs. there may also be language and ethnic barriers. Those factors probably are in play to varying degrees in the Muslim nations farther west.