When you're trying to make a world, there's going to be awful bits to it, too.
As the game's gone on in years a lot of the seedier stuff has kinda been washed away. Maybe this is because of a more focused storytelling team with a more unified direction, but for better or worse that older stuff is still there, just like how horrible things are rampant in our world's history and its today. The Moogle quests in particular weren't designed to simply be necessarily fun and cute, but vignettes to further develop groups and individuals throughout ARR that had always been there. This one's about the Courelclaws, a brigand group of poachers that are outlaws living in the Shroud.
I didn't read the story as deliberately idolizing harem and grooming culture, nor deliberately shocking or edgy. The Courelclaws are not exactly cast in a positive light throughout the game to this point, mostly just serving as villains in FATEs, levequests and sidequests where they exist at all (you can in fact "kill" the Courelclaw King in the South shroud in a FATE chain). This quest served to color them further to show that many people among what is basically another faceless 'bad guy' group are suffering because they're outcast and marginalized from a society that could be protecting them, and only isn't because of racial prejudice.
Spoilers for 5.4 and later expansions:
Likely, at this time the story feels worse even outside of context of the real world, because Ul'dah and Limsa have started dealing with their skeletons a lot more in recent patches. And, 6.0 had an excellent opportunity to revisit a lot of these old zones, especially with the major threat of the expansion, but it largely didn't as expansions tend to largely focus on new zones, partially due to advertising requirements (it might not have gone over as well if EW only had 3 or 4 new zones, or had them all but spent more time in ones they've been in since 2013). Given that the story's still being written, there's some chance that their story might be developed more in the future.
There's clearly a line that they do enforce, so maybe if it really does bother you and you really think it should be removed for the game, push for it: They have changed things before for similar reasons. I remember the original t9 savage achievement name was "The Crying Game," but some folks thought that reference was in poor taste. It's "Scent of a Woman" now, and I'm still not really sure how that reference is supposed to make sense... Anyways, I think the quest's most egregious factor is as others have said it can kinda come out of nowhere, but that's often how the world is.