Can you reject moral objectivism based off of personal opinions?

Are people entitled to believe whatever they would like to?  Are all of their opinions equally plausible? Russ Shafer-Landau explores ethical objectivity in his book The Fundamentals of Ethics.  I believe that "Equal Rights Imply Equal Plausibility" was one of the stronger arguments from the chapter, Ten Arguments Against Moral Objectivity. The argument given in the section begins by stating that, “If everyone has an equal right to an opinion, then all opinions are equally plausible." (Shafer-Landau 2012, 323)  One can see that this is most likely the way that most people in our society were raised; constantly being reminded by your parents that everyone is entitled to his or her own opinion and that everyone is right when they give their opinions.  For that reason it would make the first claim seem plausible without reading into it any further.  

However in order to deconstruct the argument, Shafer-Landau suggests an interesting point at the end of the section by drawing attention to the fact that this first statement, as it stands, does not really add to the argument as a whole against objectivism.  He reminds the creators of the argument that the first claim could be interpreted as two completely different ideas. (Shafer-Landau 2012, 324) Shafer-Landau portrays both sides that he’s referring to as one interpretation being everyone has the free will and right to think as they please, and then the other is the question as to whether or not the person has a correct opinion. (Shafer-Landau 2012, 324)

By referring back to the original questions I posed, I believe that one can respond to Shafer-Landau’s previous comment, as to whether or not this is a sound argument against objectivism.  The answer to the first one, in my opinion, would be yes; people are indeed entitled to and have the right to believe in whatever they want. The answer to the second question would depend what situation you are contemplating when thinking about what is or isn’t true.  Shafer-Landau refers back to a time when he was in the woods and thought he knew what kind of tree he was looking at, when in reality he did not. (Shafer-Landau 2012, 324) Of course he has the right to think about what type of tree it is even if he is wrong.  However, since his opinion is wrong it does not support the idea that all opinions are equally plausible.  It is a fact that that tree was not what he thought it was, making his opinion implausible. Equal rights imply equal plausibility is a strong argument against moral objectivism for this reason.  Since not everyone thinks the same about everything, there cannot be any objective truths.  If there were objective truths then everyone would have a foundation on which to base their opinions.  The implication here, that rights imply plausibility, is what causes objectivism to suffer and since it is a solid argument, Shafer-Landau’s reasoning for including it in his 10 reasons against moral objectivity is clear.