It's nuanced.
God hates the sinner, but he also demonstrated great love for us in that while we were yet sinners, Christ died for us.
David rightly hated people in the imprecatory psalms. David was a man after God's own heart, and those psalms are divinely inspired, so there isn't a contradiction between the instruction this action and the instruction to "love your enemy"
I think the short answer is that you hate the sinner, but carefully carefully and biblically define your relationship with the one you hate.
The westboro people aren't using careful systematic theology though, they're just provocateurs for that sweet assault settlement money.