Arbitrary is a big word. Just because the line regarding fertilisers isn't drawn the way you imagine it would be doesn't make it arbitrary. I'm sure a lot of rational thought went into, balancing the various trade-offs involved in making a regulation that's meant to serve as a minimum standard applicable in a market with 300 million residents.
The same goes for GMO stuff, it's your prerogative to redefine words in any way you see fit, but lab-GMO and breeding-GMO are a conceptually real categories and there's nothing arbitrary about differentiating them.
No I'm using the specific definition of arbitrary: "based on or determined by individual preference or convenience rather than by necessity or the intrinsic nature of something"
My point point being there is not intrinsic nature of something that can make it "organic" in the organic food definition. If one pesticide is allowed in the US and not int the EU definition of organic that is arbitrary.
So when someone says GMO it assumed to be what exactly? Targeted gene inertion? Mutagenesis? What about marker assisted breeding? Each one of these is a continuum of progression from "conventional" breeding. All of them are human induced genetic modification, drawing the line at targeted gene insertion is arbitrary.
Any taxonomy is arbitrary. Nature / The Universe does not seem to organize things into neat categories. These taxonomies can be useful but imperfect abstractions. However IMO the organic / non-organic classification is a non-useful and misleading abstraction unlike the term "room temperature".
It's not an individual preference, it's the result of a political process. There may be a continuum of genetic modifications, that doesn't mean it's unreasonable -- or even arbitrary, per the quoted definition -- to pick a point in that continuum and make rules and regulations based on that point.
The same goes for GMO stuff, it's your prerogative to redefine words in any way you see fit, but lab-GMO and breeding-GMO are a conceptually real categories and there's nothing arbitrary about differentiating them.