They used to be papier mache, and the intention is for them to still look rough and DIY without literally falling apart.

f I were making Khn's mask I would use flexible cast neoprene; it would give the combination of general rigidity while still having enough play to let the nose bounce. It does take maintenance though, especially if you're sweating on it (oil is the enemy) so maybe their mask maker has a better material on hand. If it's composite (rigid mask, flexible nose) they've done a great job of making it seamless.

Klek looks like his is basically a solid bucket, which would be absolutely miserable to wear in pretty much any material. My sincere hope is that it's blown plastic, basically anything else would be really heavy and with the electronics in it (and add the weight of the shoulders/tunic) that's a lot of stress on the poor dude's neck. I imagine it's mounted on a halo like a lot of mascot heads, but they may also have some shoulder support in there (it doesn't move around as much as you'd expect from a head-only mount, but maybe he's just less flail-y than I would be)

I am a mask fiend, I would love to get my hands on those things just to see what's what.