As discussed in previous threads, the majority of kilt wearers certainly do not want to wear any underwear under the kilt. I would agree with this as I hardly see the purpose of wearing any form of pants under your kilt.
After wearing the kilt all day and if socialising at say a wedding or something similar and drinking copious ammount of liquid then the need to run to the restroom is essential. Many kilt hirers insist that something should be worn under the kilt for basic hygiene purposes as cleaning a hired kilt can be quite a task at times.
LIDL came up with an alternative although this was not aimed for kilt wearers, during the recent Wimbledon fortnight they sold in their stores, ladies tennis skirt ( not pleated) with intertwine shorts. The shorts can be easily cut off leaving just the lycra skirt which is elasticated at the waist, this is a very lightweight garment and provides good cover for the outer kilted garment. i have now worn it several times in the last couple of weeks and found it quite unobtrusive but also fullfilling the need for a hygienic garment under the kilt