I thought the game won't just put it on sims!
Anyway, the political position trait only has gameplay when you have a sim in the Politician career.
Mainly, to win support on the cause or secure votes (Politician branch), the sim has some options to do beforehand so that winning support/votes is more successful. Two of these are "Debate Politics from Left" and "Debate Politics from Right" interactions.
When your sim does one of the interactions, they'll get one of these traits applies (depending which one you chose). This makes it so that when your sim debates politics from the opposite political view, they'll get embarrassed moodlet.
I never thought that game would just randomly assign these to other sims. I guess the purpose is with whom is which debate option successful and with whom it isn't. So, if you have sim debate from the right with sim whose view is on the left, it'll fail. Though I don't get how are you supposed to tell which opinion they have.
So yeah, unless you are doing Politician career, these traits have no gameplay effects.
