I don't think that is true, but unfortunately, it seems to be the case. As Fred notes, there are several cases where conservatives change their approach when they have a personal connection. With Mark Kirk, it was a stroke that made him realize that poor people with the same issue would never be able to recover. With Rob Portman, a gay son made him realize that he didn't oppose marriage for his son.
Why then? Is it too difficult for conservatives to imagine life for poor people struggling with a major illness or what it might be like to be gay? To be very fair, of course, the other conservatives could not wait to say that they would still oppose gay rights even if their own kids were gay. When you are in the conservative tribe, nothing loses you membership like backing off of bigotry.