As long as there are people, there will be prejudices and preconceptions. So, to assume that any society is free from them or will become free from them is misguided.
Yes racism based on color of skin is there in India, but it is more of a "harmless" kind than in the US. In US, prisons are full of black people and black people are regularly mistreated by the police. It is common occurrence in US that black unarmed people are shot by the police. In India, people may pass comments because of the color of your skin but you will not get shot because of that.
There are much bigger problems in every society that we have as far as racism is concerned. Although, there is some targeted racism towards North-Eastern people in north India, which is shameful. So, unless you are from north-east, I don't think you should be overly worried about racism in India. In India, fair skin is associated to beauty. People all over the world treat beautiful people differently than not so beautiful people. You might even be doing the same.