I think you've pretty much stated the exact opposite of my own moral-epistomological worldview.
I don't like the analogy with physics. Physical theories get tested against external reality in a way that makes them fundamentally different from ethical theories.
If you want to analogize between ethics and science, I want to compare it to the foundations of mathematics. So utilitarianism isn't relativity, it's ZFC. Even though ZFC proves PA is a consistent and true theory of the natural numbers, it's a huge mistake for a human to base their trust in PA on that!
There is almost no argument or evidence that can convince me to put more trust in ZFC than i do PA. I don't think I'm wrong.
I trust low-energy moral conclusions more than I will ever trust abstract metaethical foundational theories. I think it is a mistake to look for low-complexity foundations and reason from them. I think the best we can do is seek reflective equilibrium.
Now, that being said, I don't think it's wrong to study abstract metaethical theories, to ask what their consequences are, and even to believe them a little bit. The analogy with math still holds here. We study the heck out of ZFC. We even believe it more than a little at this point. But we don't believe it more than we believe the intermediate value theorem.
PS: I also don't think "shut up and calculate" is something you can actually do under utilitarianism, because there are good utilitarian arguments for obeying deontological rules and being virtuous, and pretty much every ethical debate that anyone has ever had can be rephrased as a debate about what terms should go in the utility function and what the most effective way to maximize it is.
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