US ideology is "freedom", that's why their government can bomb any country in the name of freedom and get away with it.
For Russia, well they were an atheist state for quite a long time, so secularism works there too.
As you just mentioned Bangladesh is mainly Muslim, and for majority of the Muslims world-wide Islam comes before nationality, and trying to enforce secularism is just a way of dividing up the people.
Our Military is strong enough to deal with those Burmese idiots, Don't think we will ever need Indian or anyone's help for dealing with them. Also, if they attack Bangladesh, they will come under huge International sanctions for attacking a "Sovereign" Nation. Also, I am quite sure Burma are more isolated geo-politically than Bangladesh.