Common meaning:

A relationship of trust and support between two people.

Hidden meaning of the Equity religion: 

Equity believers must stay pure and only have relationships with other Equity people.

Discussion:

Since the Equityists believe that all non-Equity ideas are violent and dangerous, this makes it impossible for an Equity believer to be friends with anyone who is not a believer in Equity.

Like many religions, believers of Equity are encouraged to have relationships with fellow believers and avoid getting tangled up with those in the world who do not have Equity faith. Being friends with or marrying an unbeliever can be highly problematic. If you are friends with someone from a dominant group, you could be seen as supporting oppression and that is bad.

Friendship is no longer an individual thing where you find someone else that you just seem to click with, but it is now a group thing. If someone has the right Equity beliefs, they are a friend, and if not, they are the enemy.

Basically, Equity is like a radical religious cult.