Well, it was outlawed by India in the 1950s, and the Indian constitution in Article 15 makes it illegal to discriminate against lower castes, so that would represent a serious effort not to remove it, but to mitigate its influence.

Among the Indian middle class, especially as it exists in the metropolises, one's caste has less effect than in the past; in fact, some claim that it is entire irrelevant among the young and relatively wealthy. But everyone is aware of it, even among those most committed to egalitarianism. In fact, Indian law recognizes the durable and unchangeable reality of caste, and uses caste designation as the basis for affirmative action.

And in some areas such as the Nepali-ethnicity northeast, language and ethnic background is a much more important distinguishing and stratifying factor than caste. But for hundreds of millions of poorer and predominantly Hindu citizens, caste is still very much alive and dictates one's job, status and options in life.

Additional (and admittedly anecdotal) sources: My work involves advocacy for Indian orphans, mostly of low caste.

Obligatory: Not a historian but.. I can provide some perspective having grown up in India, specifically the southern state of Tamil Nadu. Politics in Tamil Nadu has a long tradition of being associated with social justice and caste-based reservation policies (the indian equivalent of affirmative action). The big anti-caste efforts in Tamil Nadu was a part of the Self-Respect movement led by the Justice Party. As to how well it worked, that is still up for debate. Like /u/virak_john mentioned, in the major metro's of India your caste has very less effect. And caste based political parties are major power brokers in the political system. So the efforts have been successful in bringing representatives from all castes into the power structure. But in real world terms this doesn't translate (yet?) to caste being forgotten and in rural India it can continue to be a huge determinant of what kind of life you have. And to some extent it has also tranferred into Christian and Muslim communities too.