Social differences shouldn't make you question class consciousness. Quite the opposite is true, to be class conscious means to have recognized what economic class you are in regardless of any other features.
Hidden there is a good point though. Social differences can be leveraged as a means to deter class consciousness. Let's take the idea of the wage gap for example. Now both male and female workers can be underpaid. As a result, everyone is less likely to become class conscious and realize that, if they instead fight over a wage difference within their class.
