I think right-wing voters are humans – when they see someone suffering, they think “I could afford to give something up to help that person” – but they’re signed up to a free-market-fundamentalist cult that tells them that the answer to this feeling is individual charity. That if you give to good causes, that is a reason not to feel guilty about voting to slash welfare.
There are a ton of serious problems with this idea, but the most politically relevant point is that if it hurts you to see people needing charity, giving to charity over and over again will not relieve that pain; what you are feeling is the desire to support socialism.
When UK Tories and US evangelicals rhapsodize about charity, that’s what’s really motivating them. Of course they want you to help the poor! Just not as much as they want them to stay poor.