Clearly there is a lot of disagreement on this topic. I think Hume summarized the “Naturalistic Fallacy” — the idea that knowing something about the natural world is not necessarily relevant to how things should occur in human contexts.
I think more recent scientists and philosophers may not agree. I believe that Sam Harris believes that science can inform moral decisions.
But I think more than a mere collection of facts, science is the best way we have to understand the way the world is. If you are making an empirical claim about reality, you should be doing science to try and find an answer.
Where science has ‘moral authority’ is in its ability to honestly describe the foundations of a moral framework. The claim that all human life is related, and we are cousins with all creatures that use DNA to self-replicate is a claim about reality. This establishes something from which you might build up a moral authority for humanism. However, in itself I’m not sure science has anything to offer on issues of morality.