“Hate the sin, love the sinner”

The problem is that people don't actually do the second, they replace "love" with "pity." Pity isn't love, it's intolerance. If you truly love someone, you won't care whether they sin or not, you'll just love them for who they are and want them to be the happiest they can be.

Whether homosexuality is a sin shouldn't be relevant at all, sin is between an individual and their god, especially in Christianity.

The problem is that people justify their intolerance by misinterpreting or misapplying phrases like these. They think things like conversion therapy is a demonstration of love, when in fact it's a demonstration of brutal intolerance.

The root of the problem here is intolerance, not the words we use to describe something.