I totally get your concerns, but I think it does sound like great experience (in the sense of learning a ton and getting experience dealing with stuff - doesn't sound like it will be exactly *fun* but at least meaningful?), and I think time goes a lot more quickly than you realize now. And honestly, if it's truly terrible awful unthinkably bad, you can always quit - you won't be worse off than you are now. A friend of mine did a similar grant-funded DV-focused job for a year and ended up getting a Legal Aid job after; she found it a really good way to get to know people (admittedly she was working in a city and not a tiny tiny town, but it gives you a kind of hook for networking, even from a distance/online).
FWIW, when I lived in the tiny town, it took a while for it to grate - initially there's a novelty to it. People are also VERY EXCITED to see a new face so it's amazingly easy to meet people. (One question though: Is it a church town? Will there be an expectation that you attend and is that not you? Because that kind of stuff really stands out in a small town.)
And the cliche that it's easy to get a job when you have a job already is totally true, IME. So you may not need to be there that long.
Also (though this may not be reassuring) in future you can absolutely rebuff any criticisms that you are a coastal elite living in a bubble who doesn't understand any other kinds of voters.