Faris basically got it right as to why Gridania is like it is towards poachers - the Black Shroud is a living entity, and was the domain of the elementals long before any of the five races even set foot in Eorzea.
Everything Gridania does has to have permission from the elementals first, from hunting wildlife (and often the Shroud dictates that certain animals actually have to be hunted, to keep a balance in the ecosystem), to growing crops, tree cutting and building construction. Everything has to be run past the elementals first. Hence the Wood Wailers and the God's Quiver take violations of this very serious, as it has serious implications for Gridania itself.
Not to mention, as Faris already stated, those who violate the will of the forest also risk the wrath of the elementals, a negative karma referred to in 1.0 as 'woodsin' or 'greenwrath', which is essentially a ever increasing curse, requiring a form of exorcism through ritual dance.
If this is not done, the taint on a person supposedly leads them to being 'claimed' by the forest as a 'wildling', a doomed soul forced to wander the forest. Although it should also be said that this idea is somewhat exaggerated, as it was revealed in 1.0 a large number of people that were supposedly wildlings were soon shown to be otherwise normal in every way and were just hiding away from Gridania, because to be called a wildling effectively makes a person a social pariah and shunned by the rest of society.
This is also the reason for the 'Hedgetrees' found in various places in the Black Shroud - they form a kind of magical barrier known as the 'Hedge', which is supposed to protect Gridania from excessive greenwrath (hence their protection is vital, as it should be pretty obvious what would happen if a Hedgetree was destroyed or otherwise harmed).
No doubt by the time of ARR, the damage on the Black Shroud caused by the Calamity has probably greatly reduced the potency of the forest's power, making the Hedge more ineffective, and leading to all manner of incursions which would have at one time not been tolerated (in fact, numerous npcs actually mention this - that the power of the elementals appears to be on the wane, due to the amount of monsters found in the forest and the constant raids by the Ixal, which has serious implications for Gridania).
In any event, with the forest greatly weakened it's not surprising that illegal hunting in the Shroud has increased, as the elementals power is waning and the Wood Wailers and God's Quiver are hard pressed enough as it is maintaining internal security against the Ixal, and hardly have the time to chase down poachers (hence the FATEs and quests where adventurers are recruited for this).