EDIT: But the part about it being "bad karma" to help some people and not others, that definitely sounds like somebody has misunderstood somewhere.
Belief in karma and reincarnation has got nothing to do with it. And even the victims of this system know this.
There is also some modern, relevant benefits to identifying someone's caste: it is an indicator that someone comes from a similar cultural or religious upbringing. That you speak similar dialects of Hindi. This is important when, say, marrying.
This says nothing of the caste system as institutional discrimination, but it's worth mentioning that caste is not "purely" an economic/political bit of culture.
* http://en.wikipedia.org/wiki/Dalit
* India Untouched - http://www.imdb.com/title/tt1552060/
* India's broken people - http://www.youtube.com/watch?v=sxJr0UlcNTA
There is whole sect in India which is segregated, tortured everyday for being born as a lower caste and it does not even end with their death. They have to clean others' feces by their hands (yes even today) and this is considered a norm. Rich, higher caste still instill this in their own kids to be wary of the "dirty people". Kids born into Dalit families are reminded of this by not letting them eat with other kids, not letting them wear same clothes and being asked for their caste again and again. This system is kept alive.
This all still exists and is in abundance. Point to note is that this is not just in rural, uneducated parts of India. Honestly, the concept comes from Hinduism. As a major religion for centuries, it has a code-of-conduct by Manu to divide the society into 4 major parts. But now it is a part of every sect in practice.
It exists and it is social.
I once got stopped by a couple that gave me a story about being left away from home and no means to get back etc... I gave them Rs.50 and they kind of stared at me with bewilderment like "that's all you're giving me"
(And keep in mind that I'm not a white guy standing out in the crowd - I look just like every other Indian on the street :) )
Small things like this make me slightly more reluctant to give money to people on the street. I prefer to donate via charities that I help out with instead.
I have been discouraged from helping people, mostly for the reason that it could turn out to be more trouble that it's worth, but I have never been given this reason. Also, your explanation makes no sense from a theological perspective. I've always been taught that helping people will earn you karma, so it's in your selfish interest to help those in need.
Here's an excerpt "If someone is born in an unfortunate situation, for instance into a very poor family, we explain it as due to past bad karma. We try to do more good karma this life in order to ensure we have a better rebirth. Is this chasing after happiness in life after life correct?
Some people say, "Those people are poor because of their bad actions; therefore they are morally inferior. We shouldn't try to improve their situation because that would interfere with their karma. Rather, they should accept being in a lower class and try to create positive actions so they will be rich in future lives."