1) When Pirsig says that everything, according to SOM, is either a subject or an object, he sometimes takes this to mean only substance. For some arguments he can get away with this, and he uses this definition wherever he can, because it makes the current metaphysics seem the most extreme and ridiculous.
2) When he can't do this, he makes the SOM define reality to include only what science has blessed as real. It's this definition of SOM Pirsig usually adheres to. So for example, even though gravity is neither subject nor object (substance), the subject/object metaphysics says it's real because science says so. He also takes the approach that if science hasn't weighed in on something, even if it's a thing science has no business speaking about, then the thing is not real. Also, depending on the argument he's making, what constitutes science varies. Sometimes it's limited to physics. Sometimes it includes anthropology. Sometimes he equates being scientific with simply being rational or objective.
3) But even this doesn't suffice to cover it. Sometimes SOM refers to the subjective/objective split, the belief that a thing is either one or the other and the twain shall never meet. In this version of SOM, you believe that subjective things are real, perhaps more so, than objective things, but you are forever saddled with the vexing mind/body problem and the inevitable slippage into solipsism, which even dualists find distasteful. Pirsig is a recovering SOMist of this variety, and is not too critical of it, even though he suffered mental illness struggling over its consequences.
So SOM is a hodgepodge of things. I certainly think that Pirsig's conception of the SOM is a strawman. I think the current Western metaphysical belief system is not captured accurately by SOM. Both 1) and 2) are too narrow and 3) is clearly a minority position. The closest representation lies somewhere between flavours 2) and 3). My opinion is that Western culture could stand being nudged toward 3) a little bit more, to the extent that nearly all philosophy students would agree that, for example, humour is real.
What I find troubling though is that the SOM appears intentionally misrepresented. Pirsig is probably too smart to make such errors, plus he admires the Sophists methods of rhetoric. Too bad it borders on sophistry.