I would say that one part of the answer to this question would be the growth of information technology. The ease with which information is shared across the world through the web, Skype, Twitter, and Facebook have helped to make the absorption of different cultures a distinct part of reality in the modern setting. Indian culture and Western culture have embraced a sort of cultural exchange with one another, whereby both have absorbed aspects of each.
Indian culture has seen the emergence of Western fashion and Western brands infiltrating so much of the culture. Western brands like Coca- Cola, Pepsi, Mountain Dew, KFC, and McDonalds have become a part of the Indian fabric. They have become appropriated so much that these brands do not seem "Western," but rather something a part of the Indian fabric of society. The growth of music channels that follow the MTV mode of broadcasting, as well as Bollywood films paralleling Western films are increasingly evident. Even some of the issues that used to be seen as "taboo" such as sex, women's hygiene, and communication between couples are disappearing. Now, condoms can be purchased in full view, without the "stigma" that used to be there. Women's hygiene products are openly advertised, in comparison to the times when a woman had to sheepishly approach a shop owner for "pads" and was given them in a brown, non-descript bag. The nation's first lesbian couple married and sought protection from the police, which they received, when they received death threats from their family. This is a reflection of the West. When US Secretary of State Hillary Clinton shakes hands with Congress leader Sonia Gandhi, it is a reflection of how both cultures have come to understand that women in the role of political leadership is a part of both nation's historical footprint on the world. These are conditions whereby Indian culture and been influenced by the West. The transfer of information, the global reach of job markets across both cultures, and the basic idea that cultural transfer and exchange is much easier in the globalized setting has helped to leave an indelible Western footprint on much of the urban setting of India.
However, there is another side to this story. I think that a great many of these social changes are only directed at the urban setting of India. Majority of the nation is in a rural context. In these areas, there seems to be little permeation of Western thoughts from abroad. Western culture does not stop the threats of "honor killings" of the lesbian couple. There are many areas in India where the concept of a woman continuing her education when reaching "marrying age" is simply unacceptable, as is a woman working. Certainly, Western culture is evident in the fact that nearly everyone, urban or rural, owns at least one, if not more, cell phones. Satellite dishes are everywhere, even hanging on homes made of thatch. The question will be how the influence of the West will be felt all over India, and for this, I think that an indigenous approach is needed. For villages and rural settings where there has been an intense reverence for their own traditions as long as time has passed, the adoption of Western ideas and approaches will have to come from within. Certainly, as globalization takes greater hold of Indian culture, the need to address how all of India can advance, and how to avoid a "digital divide" is going to be essential.