There is the no iron core/fractional percentage gang which bases their theory on the observed sun, but this conflicts with the common cloud theory of solar system origin, which is basically there was enough iron in the proto cloud to provide iron cores for most of the inner planets and you are telling that you think that most of this iron did not end up in the middle of the sun.
then at the far end of the spectrum is the crackpot "the solar system is a second generation(minimum) system, some star must have exploded to form the metals we see, the core of the sun is probably the stellar remnant of the first generation system and is mostly iron"
But really I wonder, all our observations of the sun are of the upper atmosphere, and more importantly the light emitted by the upper atmosphere, if earth was observed the same way you would conclude it was mainly made of nitrogen.