Common meaning:

Process that is impartial and honest.

Hidden meaning of the Equity religion: 

Not possible in the current system, so for now we need to be unfair to individuals in dominant groups.

Discussion:

Equity theology teaches that it is not possible in the current oppressive system to be fair, because there are built in advantages for members of dominant groups. As a result, our goal should be to make things fair for groups, not for individual people.

Not only is this type of thinking about balancing groups instead of being fair to people deeply flawed, but in the end it will exacerbate ill will between groups, leading to real violence. 

The religion of Equity does not believe that autonomous humans exist. All we are is representatives of the groups that we are a part of. Since groups exist and people do not, what matters is how we treat groups, not how we treat individual people. If groups have experienced unfairness in the past, that is all that matters. We need to be unfair to individuals in dominant groups today in order to balance fairness between groups.

When the Equityists say they want to make things fair, they really mean they want to make things unfair.