I reckon that the beastly races will have shoes/boots that magically adapt to their mold (whatever that may be). I also think that underwear will be mandatory, no matter what your race.

Try watching Animal Planet Big Cat Diary sometime.

Don't think they should have underwear as there would be nothing visible regardless. Boots I feel they should have their own, though I foresee it being like the Trolls in WoW. On most races they look just like normal boots, on the more beast races/Trolls the boots automatically look like that races specific boot model.

How about Khajiit?

Not sure about now, but before they were part of the Empire, a Khajiit wouldn't have been seen wearing underwear like in Oblivion, because they considered it "highly indecorous" to not have their torso completely covered.