The MKpedia didn't tell me why.
The man who started the Shirai Ryu was originally a member of the Lin Kuei, he defected from it (I don't remember why) and based his clan's color on yellow, as a way of mocking the Lin Kuei's blue garbs, somehow.
I'm pretty sure this is from Deception's Konquest.
*Side note: To this day, Takeda's reasons for leaving the Lin Kuei, as well as the exact circumstances behind his demise, remain subject to speculation, as they have yet to be fully addressed in canon. While Tobias and Vogel still remain silent about the circumstances regarding Takeda's defection from the Lin Kuei, it is speculated that the Lin Kuei themselves are responsible for his death, as evidenced by the fact that we know from Sub-Zero's MK3 bio that desertion is considered tantamount to treason by the Lin Kuei, and therefore punishable by death. I believe this speculation is strengthened by the fact that the war between the two clans persisted for centuries beyond Takeda's death (my take on this is that the Shirai Ryu swore to avenge their founder's death).