A class is just a group that shares attributes. You can subdivide people (if people is your interest) into any number of classes to suit whatever point about them you are trying to make. Some divisions will be more useful than others for explaining the way the world looks, but the division itself happens not out in the world but in the process of explaining the world. Keep that in mind when you identify as 'working class' like it is a name you were born with, like a genetic marker or even a culture you were educated in, because what it is in reality is a group defined by their relationship to the means of production for the purposes of defining them separately from others with different relationships to the same and nothing more

Working class solidarity is thus not defined by talking right or being nice to the little guy or identifying yourself correctly, but by understanding that you share with others in what Marx defined as the 'working class' a specific set of attributes that amount to overlapping interests - namely the counteracting of the interests of the other class.