Racism is rampant in all aspects of the industry.
Actually, quite a few people have said this about the industry, and to little avail. It's a problem that's built into the structure at all levels of the business. And the racism has a shitload of outlets that goes waayyy beyond obvious bigotry like Galliano's rants and Vogue Italia promoting "Slave earrings."
The main goal of the fashion industry is to provide the ideal visual, and the well-documented all-white casts of runway shows is a pretty f'd up notion of doing just that. Think Vogue Italia's choice to put a Chinese model on its cover will change this? It's a step, but literally 99% of Vogue covers are graced by white women.
The language of the industry is another domain of racism. Model bookers know that a client looking for an "ethnic" look means a black girl. On the writing side, waxing romantic on Americana and harking back to the good ol' days is selectively remembering an era when civil rights did not exist for certain people and race-driven violence was an everyday possibility.
Diversity is seriously lacking in the people who control the conversation that reaches the audience. Google the names in the mastheads of influential publications and you'll most likely find nothing but white bread. Also, how many widely praised black designers can you name? Is this a lack of awareness on your part or because of the barriers of entry for minority designers?
Obviously, it's not just the fashion world that racism is confined to. But in an industry that is so high-exposure, it would certainly help the larger conversation if tangible improvements to eradicate the problem were taken instead of small token gestures. There is no one fix-all solution, but full awareness of racism's frequency and commonness in the fashion industry is definitely a progressive step.