Objective morality is simply the concept of something being wrong in every instance no matter what. Rejecting that concept does not mean that you also reject the idea that things can be bad under certain circumstances.

I do not believe that rejecting objective morality has any bearing on whether the individual believes in or follows any kind of subjective moral code.

Pointing out that an action is not objectively right or wrong does not mean that one condones or supports that action. I believe that it is wrong to hurt somebody else's feelings, but that is entirely subjective; there is nothing objective about it. This holds true for everything- good or bad- that can be done.

Oh god was that a blast. Some people get so confused by simple, simple things.

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No, objective and subjective morality are in fact two distinctly separate things. Also there are no objective, or absolute for that matter, morals.

"... if an action is not objectively wrong, it is not subjectively wrong either"

I think the contrapositive is less confusing so that's what I will deal with here:

"if something is subjectively wrong, it must be objectively wrong" (1)

I do find there's still room for some misunderstanding though. Let's narrow this sentence down a bit. Let's first assume that we are talking about morality from within the bounds of one specific subjective morality and one candidate for an objective morality. I.e. when I say something is subjectively wrong, I am picking out a wronghood from one specific subjective morality and comparing it to what a candidate for an objective morality states.

Taking for granted that the middle is excluded in morality (something is either morally right or wrong, there's no third option), the only possible scenario where implication (1) can hold is when the subjective morality is equal to the objective morality. The converse holds as well, If the subjective morality is not equal to the objective morality implication (1) can not be true (in that case one subjective wrong would be translated into something that is not objectively wrong).

So the discussion is contingent on whether we believe our subjective morality maps identically to an objective morality. There are some obvious ways of rejecting this. The approach Cartmans suggests is to reject the notion that an objective morality exists (objective in the sense of an mind independent morality) . To reject the existence of such a morality obviously means that implication (1) can't possible be true, because it's always the case that a subjective wrong is not an objective wrong.

Even taking the existence of an objective morality for granted it's still possible to show that the implication is not true. This could be done by showing that the subjective wrong does not align perfectly with the objective wrongs, i.e. one subjective wrong is not an objective wrong. For instance, I might believe that it's wrong to cheat in a snowball fight, but it's not so clear that it's objectively_ wrong.

So in essense, the only case where you would agree with implication (1) is if you are so deluded as to think that your morale code is objectively true, in which case you fit the same category as journalist beheading fundamentalists and people like Hitler.

Even taking the existence of an objective morality for granted it's still possible to show that the implication is not true.

As one who seeks to define morality by objective standards (I believe in objective morality), I am very aware that subjectively determined moral codes exists. I am also aware that one may fail to see the objective standard that underlies a moral foundation while still maintaining a subjective moral code and recognizing that it is in fact subjective. Rejecting objective morality while embracing subjective morality isn't only possible, it is by far the norm.