the idea that one who explicitly thinks "If i think X is right, then X is right" can think that anything is right.

That's relativism, right there - the idea that rightness is not only socially determined, but individually socially determined.

It strikes me as unfair to accuse Eliezer of having his own private meaning of "right" that isn't in accordance with the common one

In what way? He has explicitly forwarded the idea that rightness can only be understood in relation to a particular moral code, with his talk of "p-rightness" and "e-rightness" and who knows what else.

That is incompatible with the common meaning of rightness.