The reason I think Republicans hate poor people has nothing to do with their policies. It has everything to do with their rhetoric. When Republicans like Orrin Hatch say the poor are lazy and need to help themselves, despite the fact that the working poor are very hard working, then what on earth do you want me to conclude other then Republicans don't like poor people?
Sure, I think that's a fair conclusion that any rational person could come to in response to a comment like that. Obviously Hatch was wrong. I, and a lot of conservatives, blame the government for the failure of welfare policies and the sustained poverty we see, not the poor themselves.
Not to excuse the vitriol of course, but I think bruhgmger2's point is an important one. A good-faith defense of free market/small government policies should be that those policies help life people out of poverty. But the prominent defenders of free market/small government policies haven't generally tried to make that argument and have instead focused on the
rights of people with money. In doing so, the idea that such policies actually do benefit poor people has generally been ignored or forgotten. As such, fewer people believe it, and it doesn't generally look like elected Republicans really believe it either. That presents both a challenge and an opportunity to people like yourself who really do believe free market/small government ideas work for the common good. The challenge is that, unfortunately, you will have your motives impugned. The opportunity is that you get to present people with ideas they are not accustomed to hearing. And when people change their views, it's not normally after hearing the same argument for the 10000th time, but from hearing a view from a fresh perspective.