I would give the following guidelines:
- Don't assume that your people will all vote the way their aristocrats would vote, and remember that by and large in LOTR you only see the aristocrats.
- Instead think about lifestyles - what is an ordinary horse-breeder in Rohan likely to want from life? What about a pub landlord in Bree? Or a small businessman in Dale? Initially they might well be social conservatives (though I'm not sure they all would), but they may well also be amenable to voting for things that will actually make them better off.
- Nationalism and internal warfare I think we should semi-discount - Gondorians may be more likely to vote for fellow Gondorians, but obviously if you assume everyone's priority is to break back up into their own kingdoms the whole thing breaks down a bit. So yeah, regionalist sentiment I think will exist but vary, and some people (like the Dorwinions or the Dwarves) will be much more in favour of integration because yay for decent long distance trading.
- That said, run with stereotypes to an extent; this is supposed to be fairly light-hearted. In the CTS version we had Rohirric voters parodied as Top Gear viewing heavy road-users which was hilarious and worked well.
Does that make sense?