Your main agrument of not wrestling with pigs is a good summary of the frustration at the moment but if that frustration turns into further polarization, severing of relationships and 'othering' then that's just mirroring the undemocratic elements of the cult that is Trump's base. Don't get me wrong, I've cut ties with my evangelical family and we haven't been on speaking terms for going on more than a year now and it's because of their public support of Trump and rejection of an invitation for rational, measured civil debate. We live on opposite sides of the earth, there is a global pandemic restricting travel between countries right now so there are physical constraints to means of relationship and communiction repair.
In the great debate on persuasion vs turnout, for 2020 the evidence appears to show that persuasion of independents, white college educated, suburban voters was a larger statistical contribution to Biden's marginal performance improvement vs Hillary in 2016 than Democrats urban "base" turnout.
While I'm also not enthusiastic about wrestling with pigs in my personal life, as far as getting on with moving to a better society you can't ignore rural America for two reasons. The first is that America compared to other countries is very sparsely populated, something easy to forget when you live in cities and that's not going to change anytime soon. Outside of a handful of pockets of dense urban centers in California and the Northeast, most US cities don’t have a substantial dense (>2,000 ppl/km2) urban core, but instead the population by and large residing in some type of suburb (100–1,000 ppl/km2). The real political front lines are within the suburbs — peripheral (500–1,000 ppl/km2) vs satellite (50–200 ppl/km2), rather than the true urban and rural which are actually small populations by comparison.
The second point is that part of the root cause of what created Trump white nationalist populism as a political force is an economic system that has eroded the social and human capital from the rural and urban poor. That is the economic scar that is going to find its way into politics one way or another so it would be naive to fantasize about constructing a successful political strategy that ignores this deep and painful scar.
Rural does not = conservative. They are correlated for certain reasons which have been the focus of a number of research studies and journalists and a path down that journey will also intersect with the white evangelical community, but the church is an evolving political organization that, like rural areas are not going away anytime soon either and within the church community has elements that span the political spectrum.
The most extreme elements of Trump's base can't form a national majority on their own and could only form a majority in the most rural states. There are edges of the conservative community that privately express reservations about Trumpism.
Your questions to the FB group - how to execute an outreach strategy - are good questions. If nobody has an answer, from my experience working tough problems as an engineer -- that's a signal that you are on the right trail and to keep digging further. Find the answer to those questions that nobody feels the confidence to answer.
The challenge that I see is the question of how to establish communication across the aisle. That's relationship building and its about building trust. One of the characteristics of conservative politics is that it is inherently suspicious of the source of the information. It is very selective on where it gets its information. But it isn't impossible, it just takes some time and investment and patience to listen, and be respectful for the little things and symbols of their identity that they cherish -- like sweet tea. The overton window and room for compromise is larger than what it seems from the outside once you have been invited into their space and are seen by them as non-threatening. But overcoming that hurdle can seem intimidating.
That's on a micro-level, but on a macro level I think your main logic of how to be strategic certainly comes in. There are probably a lot of houses and phone numbers that its better to give it a pass. When I was phone banking for Biden one guy said on the phone "Yep, I voted for Biden, and I got a purple dildo... where can I get more of those purple dildos?" So yes there is no point talking to people like him but keep knocking on doors.
Within these communities are charismatic opportunists that exploit (consciously or unconsciously) the authoritarian predispositions in these communities for self-enriching purposes, but there are also respected leaders and bridges - people who understand nuance and respect scientific authority. I know that sounds hard to believe but its a bit unrealistic to state otherwise.
For me these are the people I would reach out to and try to build a relationship with. It may take some time yes but its worth the investment. Look for and search for these bridges that can help to repair trust and open up the door to that kind of civil, nuanced dialogue that seems unreachable at the moment.
As far as the geographic return on investment of outreach, I would agree that it may make more sense to focus the outreach energy and resources first on suburban and outer suburbs as opposed to jumping straight from urban to rural. Particularly the suburbs since that's where there is a broad mix of identities and that balance should help to create an environment that is more favorable to nuanced conversations. At some point depending on how literally you interpret rural you are talking about reaching out to cows so a more precise problem statement is what I would call "peripheral suburbs" and "small towns"
Vox, What is the future of evangelicalism
https://www.youtube.com/watch?v=MG_l0-IJ_BQ
I grew up in the Westboro Baptist Church. Here's why I left | Megan Phelps-Roper