Yeah there's a difference you aren't seeing - they just conceived the faction, there's no history and attachment,it takes 10 minutes for them to make the alterations people are asking for that will keep the premise and tag identical and not resemble IRL problematic imports. After the specifics people brough up and Karlotta specified it seems a little too on the nose with that specific IRL group - both name and symbol, it takes no effort to name them to e.g. Humanity Preservation/Protection Fellowship/Federation/Fraternity/Foundation and/ or use different cog graphics.
Coalition doesn't have both symbol and name, and taking away the star that's been associated with the in game assets for so long would be way more effort and has changed meaning to in game history over the years - if I am OP, I'd just make the minor changes because nothing is lost and there's no effort and I can then focus on doing my thing in preserving humanity in its original form. As I said the existing name isn't even that evocative for the premise, the alterations will make it better even.
Was the same with First Armada - the tag was free and never used, but it came to my attention that a more or less dead faction used the same name we used originally as an alternative name in the past. Even though admins told us there's no need to make the change we did because it took little effort, tag remained unchanged and now nobody remembers, it hasn't been even brought up once since then and the Word "Armada" became associated with our in game identity. It will be the same if they make the minor alterations with synonyms with same initials that will let them keep same tag here - they change it nobody will even remember in a few months they had an issue with it. They keep it it will detract from their gameplay when now it take 10 minutes to make the change - just a no brainer if you ask me.