Your question has two contradictory answers, each legitimate and correct:
1) NO, you can't dress down a tuxedo. Ever. No Way. No How.
and
2) Obviously, you can dress anything up or down with accessories. A man in a tuxedo with a long tie is less dressed up than a man in a tuxedo with a black bow tie. A colored bow tie is less dressy. No tie is less dressy. A turtleneck is less dressy. A dinner jacket and jeans ( or cowboy boots, or both) may be less dressy. Sneakers are less dressy. These things are not CORRECT, but they are the privilege of the owner of the clothes. For people who only own one kilt jacket and don't have the money to get another one, it is probably better to be incorrect ( and warm) than to go without.

This will offend a lot of people, but here goes: The average member of the US public is unfamiliar with the kilt and what is correct wear with it. That member of the public is not going to notice that the slightly odd jacket you are wearing surely looks too dressy for the surroundings. He or she is going to notice YOUR KILT. If you are in a situation that calls for a kilt and a jacket, but not black tie, you may wear your BB or PC without a black tie. People who know will probably consider you out of uniform, improperly dressed, etc. But one or two of them will stop and think that you are merely being creative.

Wearing socks or not, wearing a tie or not, wearing a suit coat without its mated trousers, wearing a button-down collar shirt with certain jackets- these are all things people do every day, despite opinion ( rules) to the contrary. Think of movie stars in shorts, jerseys, jogging suits, pajamas. Look at old movies where even bums wore suits- and look at millionaires who never wear a necktie. Things change and they do because people are sometimes forced to improvise, or because someone with power and influence decides to.

If there were no change, we would all be in great kilts ( or togas or animal skins) and everybody else would be in knee breeches.