It's much easier to say we love people whose actions we reject than to show true love for them. Overall, I think the histories of mankind, Christianity and Mormonism all show our difficulty living what we teach as the ideal in that regard.
In "A Time to Kill", the White lawyer tells the Black man he is defending that they are friends. The Black man's response is, essentially, "We're not friends. You've never been to my house. Your daughter doesn't play with mine. You might see me as equal under the law, but you don't treat me as equal outside this courthouse." (OK, the last sentence is my own addition.)
In summary, it's hard to claim love for someone whom you never serve - whose house you never visit and whose children (or friends) don't play / associate with your children (or friends). With respect to this thread, I think it's hard to say you "hate the sin, but love the sinner" if you don't embrace and spend time with the sinner. In my mind, that's a fairly bright line.