This is probably a multi-mod interaction bug, between this, K2 and Space Explo.

I have Schall Inserters set to only give me short armoured inserters, and nothing else, the other two on defaults.

My armoured inserters refuse to move anything. I noticed when my turrets weren't getting reloaded, but then I checked with boxes, and items on the ground, and they still just refuse to move.

Any idea what's going on?

I have just tested K2 but not SE. (No time to try and test with more mods.)
So my findings below may not be conclusive.

K2 has added filters to my "Armoured inserter I", also to my armoured series and fast (long-range) series. (But not my integrated series.)
So you may check if this is the same case to your mod set too. Setting filter allowing your turret ammo will make my armoured inserters work.

But for why filters are added to my armoured inserters?
My mod copies from vanilla stack filter, but has explicitly set filter_count = 0. (So no filters with my mods only, right?)
I do not know the reason why K2 is adding filters to my armoured inserter series (but not every inserters, say, the vanilla fast inserter has no filters in K2.) So you better ask them.

That works, and I can just turn off the filter by setting it to a blank blacklist. I can make that work once I finish upgrading my walls (only issue is the upgrade planner)

Thanks :-)

(I'm feeling a bit dumb for not noticing that it was a filter inserter)

No worry, I am surprised how why armoured inserters are turned to have filters too. And it is easy to overlook.