@kochmann: Yeah, I think there are a lot of people who just genuinely don't give a crap about disadvantaged groups, and use liberal economics to rationalise it. There are some people who pretend to believe that eliminating the welfare state or reducing taxes on people earning over $250,000 will magically make poor people richer, whereas in fact they just want a nice tax break for themselves.
But then there are people who genuinely believe that liberal economics will help poor people. People like Bill Clinton, Tony Blair, etc pretty much reflect my own personal views on the role of the state... Those Third Way guys are who I most identify with myself. For me, liberalising markets, making it easier for businesses to hire new staff, reducing unemployment, opening up trade (and so keeping prices low) -- all these things help poor people. Economic growth helps poor people, and we can distribute the proceeds of economic growth (i.e. tax revenues) to help even more poor people. This, broadly, forms the basis of modern centre-left thinking since the 1990s. This would traditionally be classifed as "right wing" economics, but because it stems from a desire to help poor people, and is packaged with other policies designed to help poor people, it fits perfectly within centre-left economic orthodoxy. People might call Clinton and Blair right wingers, because they broadly followed Reganite/Thatcherite policies of economic liberalisation. But everything else that they did will tell you that they merely follow a new kind of centre-left politics. They are left wingers.
I don't think there are many people who genuinely want to help the poor, but simultaneously want people earning $250k per year to be taxed less than their cleaners earning $25k per year. I think it's fair to call these people right wingers, and not left wingers.
One more thing:
To be clear, I'm not really talking about personal charity or individual actions here. I'm talking about the scope of the government. There are some on the right who care about disadvantaged groups, but don't believe that the government has the authority to help them. That is, they'll give plenty of their own wealth to charity, but will still vote against parties that want to expand the welfare state and so on. Those people I classify as right wing, because their views of what the government should do falls into "every man for himself".
I don't deny that there are plenty of individually charitable right wingers. However, they are still right wing under my definitions, because they focus on individual charity, and believe that the government has no place spending other people's money. That's very much an "every man for himself" world-view, even if they aren't, personally, particularly selfish people.