"They wear white underwear."
Though はく can be written either 履く or 穿く, I think 穿く is technically more correct when it comes to clothing.
履 is more about footgear (履物) and foot protection. So 履く makes sense for shoes. I believe it's even used when talking about putting a tyre on a wheel of a car.
穿く is more about piercing/drilling (穿つ) through a hole (i.e. with one's foot/leg).
The results for したばき (as in 下 + はく) on Jisho.org are quite interesting. ^^
- 下履き / 下履 = "outdoor shoes"
- 下穿き / 下穿 = "undershorts, underpants"
I think it's just that 履 is a jōyō kanji whereas 穿 is only jinmeiyō. So maybe 履 ended up getting overstretched and used like a jōyō alternative of 穿? I wonder if it might instead be more proper to always write はく in kana for those situations and only use kanji when it's for outer footwear?
I think you're exactly right. You can find lots of articles explaining that 穿く is for things like pants/trousers, skirts, and underwear, and 履くis for footwear. But 穿く isn't jouyou kanji, and so google says:
"パンツを穿きます" - 20,700 results
"パンツを履きます" - 78,700 hits
"パンツをはきます" - 31,200 hits
Use hakimasu with things worn from your waist down (belt, skirt, socks, pants, etc.) and use kimasu with things worn on your torso (jumper, shirt, coat, etc.) There's different verbs for things on your hands and for on your head. It seems weird that these are distinguished at first but you'll get used to it owo