Let's get this right out in the open. I advocate meta-ethical subjective relativism; I assert there are no objective moral truths, only truths about what people subjectively believe. So what gives me the (objective) right to make ethical judgments?
Well, nothing. Duh. "Rights" are about ethics; I assert there are no objective rights any more than there are any other kind of objective ethical truths.
What I do have are exactly the things I assert do exist: subjective opinions about ethics. And I write about them.
I'm accused of reducing ethics to the level of "taste". First of all, I didn't reduce anything: The world is the way it is, I just try to understand it. It's not like I can make truth go away just by disbelieving it, any more than one can make falsity come to be just by believing it. Perhaps I'm wrong. But getting mad at me and calling me stupid won't change the truth, won't change my mind, and won't make me stop writing. I won't change my mind on the basis of anything but sound argument.
Secondly, asserting the equivalence of subjective ethical belief to "taste" is fallacious and misleading. It's fallacious in that similarity does not entail identity. Subjective ethical belief and taste are similar: They are both subjective. But they are not identical: tastes are those subjective ethical beliefs which are relatively trivial and which we don't extend to others. Subjective ethical beliefs are those which are important and which we do extend to others. Drawing the identity asserts that all subjective beliefs are trivial and are not extended to others. I simply deny this assertion.
At the political level, one might ask: What right do I have to impose my personal subjective beliefs on the rest of the world? It's a little more difficult to answer this question because I don't personally impose my beliefs on anyone. In case it has escaped anyone's attention, I am not the dictator of the world. Neither do I blow up buildings, murder abortion doctors nor fly airplanes into buildings. I'm a civilized person and a citizen of a democracy. What subjective beliefs do get imposed on a society is a complicated process of negotiation; no one person's beliefs are ever privileged.
Another objection that has been raised is that I assert, by virtue of approving of democracy, that if a majority holds an ethical belief, then that belief is objectively true. If you think I say this, you are not paying attention. I say that nothing at all ever establishes objective truth. Majority opinion establishes only that a majority holds some opinion, and that contrary opinions are held by a minority. As it happens, if a majority of a society holds a particular ethical opinion, that opinion will usually find its way into their law, but that's a horse of a different color: It's a (rather obvious) statement of sociological science, not an ethical judgment.
I love the truth. I love the truth more than I love my wife (and I love my wife a lot, and that she loves the truth as much as I do is no small reason why I love her). If ethical objectivism were the truth, I would believe it. But, for good or ill, it's not. As I've written earlier, we have no epistemic foundation for establishing objective ethical truth. It's just not there.
If you don't like this meta-truth, tough shit. The truth is the truth, whether you like it or not. There is no God, whether you want there to be one or not. You can't flap your arms and fly to the Moon, whether you like it or not. If you get cancer, you might die, whether you like it or not. If the sun explodes, or if the apocalyptic idiots in the White House start a nuclear war, we'll all die, whether we like it or not.
I could, of course, be mistaken. Maybe there is an epistemic foundation for objective ethical truth. All you have to do is prove it. But arguing against meta-ethical subjective relativism because it is not objectivist, because you just can't stand the idea of objectivism being false, is futile, stupid, and ridiculous.