Dragoons aren't specifically Dragon Hunters, at least not Adventurer Dragoons, the Ishgard ones certainly are but then every Ishgardian is basically a Dragon Hunter.

If anything, an Au Ra Dragoon makes more sense if they're part Dragon; Dragoons take power from Dragons (specifically Nidhoggs Eye), which is where they get the power for their Jumps. If Au Ra are half Dragon then they'd already have some of that power in theory, and thus make natural Dragoons. I actually wonder how they're going to sort out Dragoons lore, since there was a big thing about their only being able to be one at a time (lorewise I think Yoshida said we're meant to ignore other players), but then 3.0s trailer shows us a whole group of them...

As for half-Dragons killing Dragons... It's no different than any of the existing races slaughtering all the humanoid enemies currently in the game, is it? Dragons are bad so we kill them, just like Garleans, Tempered, Pirates, etc., are all bad so we have no issue with Miqo'te killing Coeurlclaws.