My personal rule (in general), is to ask the following questions before I decide:
1) How likely is there to be an accidental exposure?
2) How likely is the accidental exposure to put me in an uncomfortable position? (like will I be giving an anatomy lesson to a six year old)
3) How easy is it to clean the kilt?

SO... if I'm in a contemporary (washable) kilt, with a bunch of adults, who won't be offended if they see anything... I'm very likely to be regimental....IF I'm at school, in a formal wool kilt, I'm wearing something under the kilt (for me personally it is usually a pair of dark colored briefs so that any exposure seems to merely expose a "shadow")

But in the end what you wear under your kilt is entirely up to whomever picks your cloths out in the morning ... which hopefully means it is up to you!

Cheers
Chris