First, despite having different cultures and religions, most of the people are either from the same race or closely related races. This is similar to how western multiculturalism wasn't much of an issue back when it was only different kinds of white people, and mostly western white people, mixing together.
Second, a place like India has many tangibly different religions: Hinduism, Buddhism, Sikhs, Jains and even Muslims. But these people are all, with only a few differences, surprisingly culturally similar. They eat mostly the same foods, speak a shared language, live in somewhat similar environments and share values with each other (in the common, secular sense of what values are).
The issues with western multiculturalism are: very different races that have no intention of getting along with each other, that have little to no shared expectations, whose religions or ways of life fundamentally conflict with each other in terms of values.
To put it simply, western multiculturalism is western liberals (who are usually on a wide variety of psychiatric drugs) pretending that everyone in the world has or soon will have the same values that western liberals have, because progress. But with each passing day that looks a little bit more crazy. The pressure is mounting. As I touched upon in another thread, sooner or later that dam will break and the western leftist will just want to secede from the world.