I have no idea, this is actually quite a good conundrum. I guess it would depend on the candidate.
Lean NLP since the party would align more closely with my mildly pro-immigration, midlly anti-welfare, and anti-NIMBY views. I would probably be turned off by the federal CSP’s anti-abortion and pro-NIMBY stances, but can easily see myself as a swing or CSP-leaning voter downballot.
I wonder how the two parties’ voter bases would differ demographically, if at all. I don’t think the racial, religious, educational, and urban-rural divides that characterize today’s Dem vs GOP divide would easily map onto this party system.
My guess is that this is what a close election would look like:
CS wins the black vote as well as the evangelical vote but the NLP wins white liberals. Latinos are generally close but are almost always ultimately won by the NLP. The protectionism issue helps the NLP in the Midwest, but their more elite image (which they neither want to nor can shake off) means that CS is competitive in the region. Meanwhile, CS loses most of New England but wins Rhode Island, Connecticut and ME-02 off the backs of populist campaigning and being a good fit for the urban and disconnected rural poor. In the American West, the communitarian image of CS makes it sort of a quasi-permanent minority but it does very well among Mormons, allowing it to regularly win UT and ID. The tariff issue cuts both ways - it gives the NLP a foothold in the MW but also gives TX to CS.
Note that a number of states would be relatively close, and most will be winnable for either party.
Why do you have Indiana, the most Southern-influenced and conservative Great Lakes state, as voting Liberal but Iowa, Illinois, and Ohio in the Conservative column?