"Universalist" and "Subjectivist" aren't opposed or conflicting terms. "Subjective" simply says that moral statements are really statements about the attitudes or opinions of people (or something else with a mind). The opposing term is "objective". "Universalist" and "relativist" are on a different dimension from subjective and objective. Universal vs. relative is about how variable or not variable morality is.
If morality varies with individuals, as required by subjectivism, it is not at all universal, so the two are not orthogonal.
You could have a metaethical theory that morality is both objective and relative. For example, you could define morality as what the law says and it will be relative from country to country as laws differ.
If morality is relative to groups rather than individuals, it is still relative, Morality is objective when the truth values of moral statements don't vary with individuals or groups, not when it varies with empirically discoverable facts.
You could also have a subjective and universal meta-ethics. Morality judgments could be statements about the attitudes of people but all people could have the same attitudes.
If morality varies with individuals, as required by subjectivism, it is not at all universal, so the two are not orthogonal.
Subjectivism does not require that morality varies with individuals.
Morality is objective when the truth values of moral statements don't vary with individuals or groups
No, see the link above.
There seems to be a widespread impression that the metaethics sequence was not very successful as an explanation of Eliezer Yudkowsky's views. It even says so on the wiki. And frankly, I'm puzzled by this... hence the "apparently" in this post's title. When I read the metaethics sequence, it seemed to make perfect sense to me. I can think of a couple things that may have made me different from the average OB/LW reader in this regard: