I suppose I agree with everything you wrote, but being objective is tricky because first everyone needs to know the facts, and then they all need to agree on how to interpret the facts. I feel like, by the end of the process, it's mostly subjective. Your health example is simpler than many real-world moral conundrums.
For instance, should inveterate criminals be executed? Well, how do you arrive at an objective morality for this, without first considering whether it's possible for even a hardened criminal to be reformed, and whether it is more humane for society to pay for him to live in prison or whether that does more harm collectively than executing him would. Perhaps he should spend years working off his debt to society, but now you've made him a slave, and that's got its own moral cost.
Then one has to consider what his crime is; would murder of an innocent man be worthy of execution? Then what about murder of an opposing gang member who was shooting at him? What about dealing drugs to large numbers of people and ruining their lives? It's hard to see how facts can be used to arrive at a logical conclusion here without everyone also agreeing that factor X has this much importance and action Y does this much harm, etc. etc.
So I'm naturally wary of using the word "objective" at all. Whether a religious person follows the standards of his god, or whether humans try to agree on a secular morality, I think it's mostly subjective no matter what.
