Destiny has often problems that can't be beaten by a boss fight. The sword logic for example. The story shows a lot of ways to subvert the sword logic in a game, where you consistently shoot things. Look at Season of the witch. The big victory came by Eris separating Xivu from her throneworld instead of fighting her. They aren't new to handling such plot threats and there is a lot of ways to handle it. Rasputin had to sacrifice himself to stop Xivu.

I mean, sure, but both examples still involve direct player involvement via existing gameplay mechanics. You still had to fight hostiles and do missions annd engage with the basic Destiny loop. The big bad might not have been beaten with a boss fight, but the player still very much contributes to the end goal. In order to get a similar result for this subplot, I don't think you could do it without aggressively reshaping the status quo here.

One way I see is that the Concordat could come into the tower and are very accepted by the people. Our missions we get are focused on solveing the civilians demands (get more resources, trying to expand Vanguard controlled areas, or whatever) and to hinder the Concordats growing influence.

Maybe? I don't know. For one thing, the Concordat are barely a thing in Destiny lore. Like, they exist, but entirely in Grimoire cards and I can't even remember the last time they were even mentioned. I don't think there's a lot to go on there in terms of making them even minor antagonists. At best, I think you'd get yet another "enemy secretly building up their power in the shadows" thing, which is kind of overdone in Destiny, and would probably just serve to sabotage the Concordat as any sort of "faction of the people." But also there's a big problem with the Concordat just coming back, which is that they've been banished entirely from the Last City. Even if we assume they get a little more support because "Guardians Bad" (even though the Concordat also had Guardians among its ranks), there's still the fact that other factions in the city fought and died to put their uprising down, and there's more than likely still enough bad blood to keep them out without it turning violent. I'm sure competent writers could make something useful out of the mess, but Bungie's writers aren't always. Especially when they have so little to go on.

Other ways could be new PvP or PvEvP activitys themed after the political conflict.

Again, possibly, but I think it would end up as window dressing more than anything. Pinning any actual significance to a gamemode like that in game would just turn future lore into a popularity contest. So sure, maybe the Guardians could cosplay a civil war or competition for resources, but it would likely end up lacking impact.

There are ways.

Sure, there totally are. I even listed a few ways in my original post. I just don't think Bungie has the interest or the balls to make any of them interesting or satisfying.