>"most people think killing people is bad" can be reduced, with great difficulty, into statements about human behaviors and brain activity.
I doubt it, but in any case, the important point is that you can't do the same thing for "Killing people is bad." It's an important distinction. Most people think that homosexuality is bad, but we wouldn't want to conclude that it therefore is.
It feels like you can't do the same for "killing is bad" because people mean a bunch of different things by "killing is bad". Each piece, individually, is much more amenable to a reductionist treatment. Let me be more specific.
Suppose Alice gets in an argument with Bob, and stabs him. Is Alice worse off having done that? Is Bob? What is the impact on Bob's family, friends, and co-workers? Is society better off having a policy of arresting people in Alice's situation? And imprisoning them? Or socially disapproving of such action? When you learn that Alice stabbed Bob, how do you feel about it?
This is vaguely the lines which you'd take to talk about human morality in terms of behavior and mental states. This is not an exhaustive breakdown, and there's some parts that "morality" still claims afterwards. The point is that there's only so many things that people can mean by putting moral judgement on something, and there's nothing left when you've addressed them all. Addressing the pieces is usually done by going to human behavior and experiences.
Circling back to people thinking homosexuality is bad - we can make moral judgements about moral judgements. Statements like "'Thinking homosexuality is morally wrong' causes a great deal of pain for the people I care about."
Minor quibble: at one point, scientists believed that you couldn't prove whether or not two particles were identical in every respect. "I don't think that it's possible to prove X" isn't a proof that it's impossible to prove X. I'd rephrase that quote as "I don't know what a proof of X would look like."
>The trouble is that answering all of those questions still doesn't tell you whether it's right or wrong.
If you answer all the subquestions, then whether it's right or wrong doesn't matter. Let's take a much simpler, analogous question to illustrate the process:
"If a tree falls in a forest, and nobody is around to hear it, does it make a sound?"
The controversial part of this is what people mean by "makes a sound". It's easier to break down here because there are only two senses of the it - vibrations in the air versus the qualitative experience of hearing. Once you've answered that it makes vibrations in the air but doesn't cause a hearing experience, whether or not it "makes a sound" doesn't tell you anything about what to expect.
Similarly, if you figure out what people mean by something being "right" or "wrong", you can use those pieces to cause the things that "rightness" and "wrongness" cause without caring about the overall judgement.
I'm not sure what you mean by that. If I have a troubling ethical decision to make, I might very well answer all of your questions and still be unsure whether the action I was going to take was right or wrong.
The trouble is that answering all of those questions still doesn't tell you whether it's right or wrong. (Also, you formulated some of your questions using equally value-loaded terms, such as "better off".)
I doubt it, but in any case, the important point is that you can't do the same thing for "Killing people is bad." It's an important distinction. Most people think that homosexuality is bad, but we wouldn't want to conclude that it therefore is.