Common meaning:

Who a person is, including all of the qualities and beliefs that distinguish them.

Hidden meaning of the Equity religion: 

The only part of people that matters is their political group affiliation.

Discussion:

The Equityists believe that the only things that are real are groups and the power they contain to damage the oppressed.

Most of us understand our identity to be made up of many different qualities and beliefs, after all humans are complicated beings. Equity disagrees because it only accepts that groups and power are real, therefore the only part of our identity that is real is our political group identities.

I think that one of the reasons the Equityists react with anger when someone questions their beliefs is, from their perspective, that you are not just questioning their ideas but the reality of their very identity.

We live in a sad world when nothing matters about an individual except for the fact that they believe in politically correct ideas. This damages both them and the society they live in.