Most consequentialists adopt a "golden rule" sort of axiom about minimising suffering. An alternate formulation is about maximising agents' preferences. Generally people's intuitions about morality are broadly similar, so the challenge is to handle the corner cases most efficiently. But the basic moral relativism problems don't occur for consequentialists.
It's difficult to arrive at a plausible set of moral axioms that are going to lead you to positions such as "homosexuality is unethical", "might is right", or "slavery is ethically neutral". Very few consequentialists arrive at these positions, as far as I'm aware. Some consequentialists do end up back at what are essentially deontoligical positions, however, by re-deriving them consequentially. They argue that it's ineffective to try to reason ethically on a case-by-case basis. I think this is an empirical question about what is practical for most humans.
> If you agree moral relativism is bad, you agree consequentialism is bad.
I disagreed with this statement.
My examples were meant to say: it's possible to have "god-given morals" (and thus no "moral relativism") while still judging acts by their consequences ("consequentialism").
In such a universe, wearing a sexy dress into a bad neighborhood may be morally fine (act ok), but if this causes you to get raped (pre-marital sex bad) you're still going straight to Hell (so act ok, results bad -> bad). Conversely, if I'd kill my neighbour for no good reason (act bad), and my neighbour happened to be 1920's Hitler (results good), I will be rewarded richly (so act bad, results good -> good).
Some disclaimers: this may be based on a misunderstanding of the words you used; I don't think the universe I sketched is the universe in which we live; and of course rape is not the victim's fault, and not wearing sexy dresses may not be enough to prevent it from happening (for the sake of discussion, though, in this particular instance it wouldn't have happened if the victim had worn a more conservative garment instead.)
