I had been thinking of this difference in approach in terms of Christians who live in cities, suburbs, and rural areas. I am rather sure it applies as a general difference of all citizens, and may go some way to explain why urbanites will always naturally tend more to be in favor of more government and regulation.
This may seem odd, at first, because people in cities put up with a great deal more regulation than others, simply because living densely packed is more complicated. You'd think they'd be more sick of it. But regulation - making people do things they might not otherwise do in order that everyone can get by - is the only way things get done in the city.
So they just automatically think that is the only way anything gets done anywhere else, also. State governments are just larger city governments, and the federal government is simply NYC or Detroit or LA writ large. As those larger governments are headquartered in cities, the people in them are city-dwellers, with some suburbanites.
In the city, if you want to do something with a space you have to get the current occupants out of it. This doesn't have to be nasty - it can be bought or traded at fair value - but everything, from a neighborhood senior center to a Costco to a multistory international headquarters, involves moving someone else out so that you can go in. This involves so many permissions and clearances that you pretty much have to have someone advocating for you within the government. You need an alderman, someone who can advocate for you, offer trades and concessions in negotiating with other groups, and any number of sympathetic friends in various bureaus - or at least, people who can be made to be sympathetic because they have been wheedled, convinced, bought, or threatened.
A variation is to have someone who can apply pressure from outside. If you want to build something in NYC, someone in the state legislature or in Congress who will take up your cause will be necessary.
This does not mean that all such deal-making is necessarily corrupt. I imagine a lot of it is simple reasonableness and tradeoffs: Yes, we think having your hospital here would be good for the whole city, and we'd like to make it happen. But the current occupants have rights, and they will need places to go, and it is only fair that they get something back for being made to leave. At its best, it's a fully American free-market way of doing stuff. Everyone negotiates for his own best interest and plans can move forward.
Yet we know that this all goes horribly wrong in city after city. Because there is only a limited amount of space and a limited amount of city budget, advocates who can get you what you want are esteemed in proportion to their success, not their fairness. People who want to get anything accomplished - even good things like school maintenance and efficient traffic flow and health clinics that poor people can get to - very quickly come to accept an enormous amount of corruption, because that is simply how things get done.
They move from places like Chicago to Washington and get involved in making people do things and wonder what the objection is. What the hell is wrong with you people? We're giving something back and it's good for everyone, including you, so what's the problem?
The corruption of college sports, government contracts, and unions may be occurring to you at this point as well. This is how things get done. It sucks, but that's how the system works. If you are a Christian, these things should bother you. And I don't mean bother you in the sense of sighing that it's too bad, but in the sense of saying "maybe I need to make my living/spend my entertainment dollar/cast my vote" in a different way.
In suburban, and especially rural areas, things get done differently. Getting some good program moving involves bringing in resources from a distance to a central location, and it often takes volunteers. You want to avoid making people do things, because you are going to need their goodwill a dozen more times this year for other good causes. If you follow church stories, you will be a little puzzled at all these success-in-the-city articles over the years, with everyone getting excited that they got a parish or a neighborhood to work together to get some good thing done. Like that's not boring and normal, somehow.
Now reflect that the religious left is concentrated almost entirely in
cities: colleges and denominational headquarters. The religious right
tends to be more suburban and rural.
Minor tangent: This is also behind those denominational we-need-to-be-involved-in-the-city programs. I recall they were big in the Congregational Churches in the 60's and 70's, the Lutheran Church back in the 70's and 80's, and I've seen some of it in the Covenant as well. I have indirectly run across it from Methodists and Presbyterians. It comes from city congregations moving to the suburbs - where the parishioners now lived - and taking all their volunteering with them - because people volunteer far more for things close to home. So denominational (city) colleges and headquarters get involved to try and redistribute that. Because they live in those cities. If you speak against this, it's because you are racist. Even in NH.
I have overdrawn this. There are permissions to be gotten in small towns and freely-given cooperations in the cities. Of course. Yet I think the general description holds. What's the flip side? I think in the rural areas people will elect to have fewer programs, fewer Good Ideas, because of the effort it takes to get everyone pulling together. Problems can be more easily ignored, or at least just endured without fixing them. That's not entirely a virtue, is it? Some things actually do need to be fixed, and others really do enhance the quality of life even if they aren't absolutely necessary. In the city, lots of other people who liking fixing/interfering are all close by, so you can efficiently join forces to make/allow people to have stuff that's good for them. If you like doing that stuff, in fact, you are likely to move to the city to do it.