That's quite false. As I noted already, Enoch is pointing to the behaviour of our moral propositions and their pretense to objectivity in order to at a very basic level back up the factness of moral claims, i.e.: they behave, semantically and indeed logically as facts, and what I mean by that is, if you imput "slavery is wrong" into a logical deducation you can reach a valid and indeed sound argument, something you cannot do with something like "boo slavery", which is what some subjectivists and moral anti-realists take the content of our moral propositions to actually be. Now, to some extent, I would then read Enoch as appealing to a level of intuition or attitude towards these propositions, but an appeal to intuition isn't an appeal to popularity, it's appeal to the appearance of moral facts at our most basic epistemic access to such facts--and if your looking to do some research into the force of our intuitions when it comes to Moral Realism, W.D. Ross in The Right and the Good and Michael Huemer on Moral Intuitionism are good places to start.

It sounds semantically like "spinach is yucky" and can be evaluated logically at the same level. If you accept that "slavery is wrong" is a valid, decidable question, and not "spinach is yucky", you have been convinced by rhetoric and not reason.

So it isn't clear that Enoch is saying one thing and (in essence) doing another. He is trying to point to how on a phenomenological level, we approach the ontology of moral facts as objectively the case. This pointing is not to be dismissed off hand as an appeal to popularity, because it blatantly isn't, he isn't saying, look at all these people who agree with me, he's saying pay attention to how our attitudes towards moral facts are very similar to our attitudes towards objective facts. This, Enoch is arguing, is revealing something about the content of our moral claims that cannot be simply handwaved away as a form of dislike-like.

And we also approach statements like "spinach is yucky" like that as well, but where is the objective proof, or even evidence aside from popular opinion? It is exactly an appeal to the reader's own morality.

Part of what is so succinct about Enoch's argument is that it is essentially flipping the notion that morality seems subjective. No, Enoch is saying, look closely, it actually has the appearance of being objective.

Just like "spinach is yucky" or "Twilight is a good series". Yet none of them can actually be evaluated objectively, because the fundamental moral values "right" and "wrong" are not well-defined (and don't delude yourself - "ought to" and "ought not to" are also not well-defined). Both his rhetoric and reason are flawed.