Look, I can somewhat understand the belligerence toward rules. However, rules are often expressions of decent reasoning. Even more often, whatever practices you put in place of them are no improvement.
In this case, it is not simply that there is a "rule" against folding non-linen squares. In fact, I have never read or heard of such a thing. It is a matter of reasoning based on my observation, experience, and knowledge. If you think it makes sense to fold material that doesn't fold well and doesn't need to be folded, obviously no one will pull you over and arrest you. However, to those of us who have tread the same path, it will look like you don't know how to stuff a square. Maybe in an alternate reality where aesthetics are unlinked to sensibility and know-how, you shouldn't care about this. But that's not our reality. That you're all here wearing jackets, ties, and pocket squares is powerful evidence of that.
I actually agree with this as a general principle.
Foo, I have a question about the coat. Why are your buttons not horizontal? Is that because of the way you're standing or is that a flaw of the coat? It looks like your left side is drooping down. I'm only nit picking because I assume this is a bespoke item, so it seemed strange.