Pixar apparently did some publicity for their movie showing various Scottish Stuff.
Here’s some deerhound pictures that a lady took there.
If you look through the pictures, there’s a picture where the guy says men sometimes fought kiltless. Well… in a manner of speaking.
The basic outfit was a huge wool cloak/blanket wrapped into a kilt, and a long shirt/short robe, bunched up a little so it wouldn’t hang down past their kilt hem. Irish guys generally just wore a long shirt/short robe with either a big rainproofed-by-chemicals* frieze wool cloak or a jacket on top. Your basic man’s shirt would hang down anywhere from mid-thigh almost to a man’s knees, and included as many yards of fabric as the person could afford of nice tough linen or other fabrics. (Flax both grew wild and was cultivated, so pretty much anybody willing to go to the trouble could have a linen shirt.) The Irish favored yellow or white shirts, while the Scots seemed to have liked the natural linen colors.
So “taking off the kilt” mostly just meant taking off their coats that they wore for warmth and dryness, and fighting in their shirt that was easier to move in and easier to wash. They weren’t naked in the breeze or anything.
And yes, this means that as long as the men still had their shirts, they should have had plenty of coverage in a certain scene. But then, they shouldn’t have had clan tartans either, so never mind. 
Holinshed said that plenty of highlanders dressed in the Irish fashion, with shirts and cloaks instead of shirts and kilts. So people called them “redshanks,” because their legs got colder that way. 
There’s also some pictures of an Englishman dressed like an Irish kern, in an ionar jacket and a very short, low-necklined shirt, to improve mobility with the spear and impress the ladies. I’m pretty sure that men wearing that style did occasionally flash somebody, but they were probably also wearing some kind of loincloth for athletic reasons.
* The chemicals being stuff like honey and gunky stuff, used to make the wool stand up and keep the rain off more. One side of the cloak looked pretty much like a sheepdog or a sheep and there were huge poofy bits you could shelf over your head to keep the rain off, and then the inside was woven like a normal (albeit thick and warm) cloak. They sold a lot of these anti-rain, anti-cold cloaks in Europe, too, at certain times. But yeah, Manoloblogger probably wouldn’t like ‘em.
If you scroll down, this shows several pictures of Irish men and women wearing the shaggy cloaks in Tudor times. They were banned by the English not long after this, as being too convenient if you needed to run off into the hills. This also ruined that particular export industry to Europe, but the English didn’t care.
Keep scrolling down, and you’ll see some great pictures by Durer of Irish fighting men in their shirts — down to their knees.
