You're skirting around the issue.
> Try something contentious - e.g. homosexuality. Who has the authority to judge that?
Again. YOU do. I'm not saying that I would agree with your individual judgement if you believed that homosexuality was "wrong." But YOU have the individual, personal, moral authority to choose your value system and to judge accordingly.
"Judge" is not a dirty word. You judge potential romantic partners when dating. You judge the place you want to work. You judge the types of products that you like to buy. You do all of this according to your personal values and your sense of reason.
Law and politics is a completely separate matter from "judging." Law does not exist to enforce some socially agreed upon set of moral values and I think that's what you're getting hung up. There, you and I likely find a lot of agreement. Since politics pertains to how people organize socially, there are a lot of valid questions as to what should or should not be allowed/prohibited by "law." And people will and often do bring morality into that discussion, but fundamentally it's different from "morality" since I can think that, for example, abusing heroin is immoral but still think it should be completely legal.
> While morals can be based on analytic philosophy (which I'm personally a fan of) the fact remains that analytic philosophy may still be susceptible to Gödel's incompleteness and moreover, not everybody agrees with this approach.
You lost me here. My personal world view is that morality is a requirement of a rational mind. It is a code of values that guides you, the individual, when faced with alternatives. Should I kill the person I don't like or should I try and live in peace with the world? Should I inject heroin tonight or go for a workout? Should I obtain my wealth through fraud and theft or should I try and exchange value for value?
I don't subscribe to "universal" or "collective" morality. People may subscribe to similar codes of values, but they do so individually and independently. That doesn't necessarily mean that morality is "subjective". Values are objective in the sense that you can measure their impact on a person's life. But we are all individuals. We need morality individually because we have reason, and therefore our individual code of morality derives from our application of reason (or lack thereof if you, for example, subscribe to the belief that homosexuality is immoral).