Politics is definitely a thing here and does have to do w/ the story & narrative here.
Politics also has to do w/ your decision-making & character skills and stats (Buffs, stats, penalities, etc)...since the game's about different classes of societies & political parties mistreating each other. The murder's based around it...and you're here playing detective to figure out that, of course.
Here, we have political choices here as alignments, instead of say the variations of good/bad/neutral alignments like in DnD.
When given dialogue option, you can basically can role-play your version of Harry (that's you, the player character; the alcoholic & drunken detective) from different alignments of political parties. We don't know much about him, but you can also role-play a lot of that stuff for him in dialogue trees - i.e. his background, issues, and all of that as you go along the game.
There's 4 of political parties and you can do it how you see fit - i.e. from a communist point of view, fascist point of view, liberal point of view, or no real alignment to any sort of politics. It ain't telling you what they are up front (most are named a bit differently purposely, as it's kind of trying to be subtle here), but you can figure this out & what's actually what.
I ain't touched the Final Cut yet, but there's extra quests I guess based around even more political stuff, which were cut from the OG version of the game. I'm gonna have to check that out, at some point - the extra quests and the full-blown voice-acting.
This article explains it very well -
https://gamerant.com/disco-elysium-final-cut-political-alignments-work/