From eyeballing the survey results, we might expect the worst ideological conflicts on LW to be those current among libertarians, liberals, and moderate-to-mainline socialists, and especially those that're interesting to nerds with those affiliations: not, for example, abortion or immigration, where one camp's almost exclusively conservative. And indeed, the most heated political arguments on LW that I remember have dealt with radical feminism, fat acceptance, the treatment of women in nerd culture, and anything vaguely associated with pick-up artistry. Nothing economic, which is a bit of a surprise, but maybe it's easier to cast those issues in consequential terms -- or maybe taxes just aren't sexy.
The ethno-nationalist wing of neoreaction has also caused problems, but I think that had less to do with the subject matter and more to do with the poster: long-time SSC readers may remember him as Jim.
For example, what would be inappropriately off topic to post to LessWrong discussion about?
I couldn't find an answer in the FAQ. (Perhaps it'd be worth adding one.) The closest I could find was this:
However "rationality" can be interpreted broadly enough that rational discussion of anything would count, and my experience reading LW is compatible with this interpretation being applied by posters. Indeed my experience seems to suggest that practically everything is on topic; political discussion of certain sorts is frowned upon, but not due to being off topic. People often post about things far removed from the topics of interest. And some of these topics are very broad: it seems that a lot of material about self-improvement is acceptable, for instance.