As examples (as "taking charge" can take multiple forms across mutiple goals): table and/or moderate meetings to come to consensus on goals, coordinate members for coordinated actions toward social goals, source funding for operations if funds are needed, speak on behalf of your group (or coordinate group messaging) toward other groups. To name a few generic things. Specifics depend on what you want done.

To try and sum it up: "taking charge" is providing impetus, and potentially aligning community power, toward making headway to some social/political goal.

I was going to bring in something I saw in a different thread but then I noticed you were already there.

You seem convinced that "leaders" are necessarily authoritarian. I do not believe that, so there's not going to be much point to this.