Class in Marxist terminology is defined by the prevailing relations of production, either social or technical. So, saying that inequality is driven by "class" is but another way of saying that economic fundamentals (such as, according to Marxists, the ongoing concentration and centralisation of capital, or the tendency of the rate of profit to fall; non-Marxists may of course point to other dynamics as more relevant!) are driving inequality. It's not clear what would be inconsistent about this.