Thanks!
I've never seen the hats come up as an item I can modify in workbench mode. Helmets, yes. Hats... no?
Yes, there are several hats that you can modify with the ballistic weave. It's intended. It's also incredibly unrealistically overpowered, but there's a ton of overpowered stuff in this game.
I wouldn't really call it 'god mode.' You can put ballistic weave on the fatigues and not armor a hat. If you want an armored hat that isn't quite THAT armored, you can simply put a lower rank version of the ballistic weave on it.
Why can't you just use a lesser variant of the armor? If you think it's overpowered there is a simple solution right in front of you to make it armored, but not quite so powerful.
The damage/energy resistance of the Mk I armor is 30/30, which is significantly less overpowered than the Mk V. It seems to me that this is a solution to your problem, but suit yourself.