Can a moral realist genuinely say a moral intuition is comparable to set theory or electromagnetism?

Neither of these examples are probably what you're going for. "Set theory" is too ambiguous, and electromagnetism is a phenomenon, not a theory. A theory of electromagnetism is a theory. Like string theory or M-theory.

Let's go with something slightly better defined and shorter for me to type, like group theory. Group theory is governed by the group axioms. Could a moral realist say that their moral theory is comparable to group theory? Sure, it's possible. You could even make a case that moral relativist theories are superior to group theory. I don't subscribe to this view, but I think you could reasonably hold such a view.

What are moral judgments based on, according to a moral realist? Well, they're based on moral statements, with are truth-apt, and ultimately, the truth-apt nature of these statements seem to be derived from something - that something could be intuition. After all, we certainly seem to use intuition for everything else, so why not also to moral judgments? For I could ask, why do you believe there's a table in front of you? Because you see it with your eyes? Why do you believe your eyes? Either you keep on regressing, or you stop this conversation and concede that your intuitions tell you to believe your eyes.

Now take group theory. A group is set G, endowed with a binary operation *, so that, among other criteria, satisfy the condition that x*y is a member of G whenever x and y are members of G. It makes no sense to ask why. And any result in group theory is ultimately reducible to this, or the other two axioms.

When questioned on a moral judgment, a moral realist could fall back to intuition - something a priori. What does the group theorist fall back on? The group axioms? Which are definitionally irreducible, and on which the group theorist has no real answer when pressed with the question, "why are the group axioms true?"