Now then... the main issue is that our primary way to interact with the game world is "kill stuff". You kill stuff to level, to progress quests, and in general to do nearly everything. The body count is staggering, but most of them are nameless random things. If you added them all up, though?
In the real world, the WoL would be seen as a lunatic lethal weapon that has to be kept on a tight leash all the time because of their penchant for killing everything in sight. Because in the real world, the primary way of interacting is NOT killing things. You don't gather fleece by eradicating the local population of sheep. You do in the game. So there's a mandatory suspension of disbelief that the game mechanics that require killing tons of pointless stuff effectively don't count in your reputation.
I tend to think the only way you'd see things turn against us in Eorzea is if we start acting overly independently. It's a cozy relationship with the leaders right now. We're their unstoppbable super weapon, and we more or less go along with what they like us to do... even when the problem is at least partially self inflicted (see: Limsa and the Kobolds). We take sides, and the side we take is theirs. They're pretty happy with that and will not toss out their super weapon.
If we ever started acting independently, though? That would be a different story entirely. A WoL that has no problem telling the leaders of Eorzea that they're wrong and refusing to help because of that would be seen by said leadership has far more of a threat, and that's when they might decide we're more trouble than we're worth.