No, but you ARE responsible for doing something about conditions as they exist now. And if you do nothing other than seek to pull attention away from racism, which sits at the very ground of classism, you not only fail to do what needs to be done about racism, you fail on classism as well.
It's no accident that, for the longest time, it was virtually impossible for black people to become union members, and even when they finally did enter, they were excluded from the top levels of leadership.
And frankly, that's one of the major reasons that labor unions have shrunk, and by that become irrelevant.
You cannot address classism without addressing racism. Period. End of.