If a badminton tournament has a reasonably large prize money and attracts attention from the media, the officials usually wear shirts sponsored by the tournament sponsor.
Let’s take big tournaments such as the Li Ning China Open as an example; the officials involved in the tournaments wear shirts given by the official sponsor of the tournament, Li Ning.
In this case, all the shirts worn by the officials will be uniformed and will usually have the Li Ning brand imprinted on the shirts. However, that’s the case for big badminton tournaments.
In smaller badminton tournaments held regionally or within a club, I doubt there that there are standard uniformed shirts given to the officials.
In fact, the organiser of these small tournaments might not even hire line judges since the prize money and sponsor wouldn’t be large enough to cover the administrative cost of looking for volunteers (officials).
If line judges were hired in smaller tournaments, they usually would not wear something too formal, though they would be required to wear something decent for the tournament.
The colour of their shirts shouldn’t be too bright or fancy otherwise it may distract the players during a game.