Confusion is their tactic. This is what happens when there is an uneducated or poorly educated electorate.
Not the least confusing is the metaphysical commitment behind the phrase. How can you hate the sin and love the sinner, since the sin only "exists" as an human action. And they don't hate the idea of sin, in fact they're quite attached to it. So they must propose a Platonic, abstract Sin, sin as it exists in itself independent of the world; for in the world, sin is always a human action, even if that action is just a thought. It is this metaphysical stand point that I take as an abdication of the responsibility involved in personal ethics.
Myself, I don't believe in the concept of sin.
Plato asked whether something was good because it was loved by the gods, or was it loved by the gods because it was good? There is no good in itself, independent of good things, actions, etc.
The same mistake is made with the idea of sin. Qualities are intrinsic to their physical matrix.