In terms of immigration, even in Canada (very open to other cultures, more tolerant of them than the US), to become a citizen, there are tests to be passed, including either french or english literacy.
This is to ensure that all citizens can communication with one another, and also, to understand local laws. And, essentially, local customs.
In Canada (and the US), this means people are expected to not be racist, or biased, and there are laws against this.
One may debate the effectiveness of these laws, however my point is that once here? People caught behaving if there is a caste system here, will be prosecuted.
Beyond this, public schools, TV, movies, etc teach that all are equal. Sometimes, it takes a third generation immigrant to be "fully" localized, but eventually the parent culture is but a distant memory.
This is reinforced by the surrounding culture, which doesn't care about caste systems.
So my point is, we don't care, and we should not care. What we should do, is simply take applicants and be done with it.
You do not have to apply through your government, you can get a job and apply directly.
Now, are there Indian immigrants in the US, with consulting firms or companies, only accepting applications based upon caste?
Well, that's discrimination, has nothing to do with immigration laws, instead employement laws, and can be prosecuted.
And yes, it can be proven.