Ironically them being the same race but looking different is kind of undercut when you consider the Lost Hunters being usages of the Jungle Hunter and City Hunters mold with different paint applications. It also doesn't help modern makers because the guys in the garage don't have to fit mechanical bits into it and there is no direct reference to the face because the only thing that survived was the Greyback's head. They threw all that other stuff out. Meaning all you can get is approximations and guesswork on top of the things the studio tells you to do. You also got separate unmasked heads for the original films which means that what you're basing things off of might not be the right head because they do different things or have different static positioning of the mandibles.
I'd imagine artistically its to differentiate individuals, but from a practical point its more likely because unlike in the older films the mask isn't fitted to the head, hence the mandible configuration. Scar's head was too flat for that so I doubt that was an issue, but for damn sure Wolf's didn't, and Fugitive only needs to have it on for part of the lab escape and then be removed by Upgrade which was more CGI then practical FX. The helmets and face are also developed separately from each other so even developmentally they can't account for positioning of the mandibles.
But then why not do it when they have it off?
-Scar was meant to be more emotive thus his mandibles going everywhere. Not to mention him being more heroic than prior appearances and thus you want to draw attention to the chin.
-Wolf just needed to roar and emote in reaction to the PredAlien, otherwise he's obscured in the crashed ship.
-Fugitive does on his CGI model, but the practical FX doesn't require that because he doesn't wear the mask for any extended period of time when a face reveal is needed.
That's a big part of the reason you have half-masks for these films because the mandibles can cause the helmet to pop off or not fit entirely (both of which occurred in 2010's Predators). Practically speaking you'd have to account for this during development of the face and have the helmet sculpted over that in order to fit it properly but that just doesn't happen on these films which is why its only implied. And even then it doesn't mean it has to sit in that configuration.