Agreed: Planescape's faction represents ideologies, philosophies and world (... multiverse?)view and societal view that's political by nature. Their label are just not a 1:1 match with our world.

And in Disco Elysium (in least in my playthrough and my impression) everyone gets criticized equally at some point, even though the writers are nostalgic communist. But it doesn't feel to me like blatant propaganda.

It's "political" in quotes. In the sense that there are factions, and they represent mostly evergreen moral and civic ideas either real or fantasy (the religious fanatics, the militaristic autocrats, the death obsessed). Disconnecting them from reality, from the early 21st century political obsessions and framing allows for a much more long lasting approach and, frankly, a lot less preachy.

Since DE takes place in a world that’s meant to very much mirror ours, how would you deemphasis the political content? Would you just replace it with fictional ideologies? The difference with Planescape: Torment is that the latter takes place in Dungeons and Dragons where everything from history to economics to the rules of physics are completely different. Disco Elysium takes place in a much less fantastical world that’s reminiscent of our own; you’re going to end up with familiar conflicts unless you were to inject a lot more fantasy-sci-fi gimmicks to change how life operates there.

I would have not given the scriptwriting to terminally online, politics obsessed people. For DE it looks easy to fix, just don't have so many characters pontificating about communism or whatever, and not so much internal dialog about it. Cut it by 50-70%, be it a minor theme, focus more on the case, done.