Some Christians claim to oppose homosexuality by saying, "hate the sin, not the sinner." Is this a meaningful distinction? Is it a cogent defense against accusations of homophobia?

Yes and No. (I'm a philosopher. What did you expect?)

Yes, it's a perfectly reasonable distinction. Suppose your sibling or parent or child (as makes the most sense to you) were to murder someone. I hope that you would find what they had done to be horrible and worthy of moral condemnation. But that doesn't mean that you have to think they are horrible. It doesn't mean that you should stop loving them, or stop supporting them. In fact, I myself think that it would be horrible and worthy of moral condemnation if you did stop loving them, or stop supporting them. So, when (right-wing) Christians say things like, "Hate the sin, love the sinner", that's what the sort of thing they mean: You can love this person, even if you think that they are doing bad things. We should all agree with that.

But no, it's not, by itself, a cogent defense against accusations of homophobia. The reason it seems like this might be a 'defense' is that the (right-wing) Christians say that they don't condemn people who are not heterosexual. It's only when those people engage in non-heterosexual behavior that they've got a problem. But this just misses the point. The issue, or so most of us thought, was precisely whether homosexual behavior was morally problematic. And the charge of bigotry is based upon the kinds of reasons opponents of homosexual behavior tend to give for their views, which, in my experience, have little grounding in reality and are based upon little more than prejudice. That's where the charge of homophobia originates, and "Hate the sin, love the sinner" doesn't being to answer it. To answer it, one needs to give some reasons to think that non-heterosexual behavior is wrong that aren't grounded in prejudice. I've yet to see them, myself.

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