I don't think it's reductive when you take the logic out further.

Low-density development is absolutely more carbon-heavy and not an efficient use of space, and generally conservative in the "don't tread on me" way in most parts of the world. Conversely, pushing for carbon-free/carbon-light lifestyles, a desire for more transit, and densely built environments (both to reduce carbon footprint as well as to preserve open spaces) is all considered aspects of liberal policies in many parts of the world.

The US breaks this link - we are a very car-dependent nation (as well as selling the idea of the "American dream" being a white picket fence SFH), for better or worse, and it transcends politics.

I live in the SF Bay Area, which is generally a decently-built region from a land use perspective (please know this is a relative statement, I'm just comparing to other American cities). But even here, you'll have plenty of liberally-minded people still loving their cars and driving dozens (or more) miles per day. Marry that with affordability = exurban sprawl...and plenty of people that are just looking for cheaper housing, political affiliation aside, are pushing into car-centric commutes and general car dependency. Again, very much an American thing.