"How can communities of faiths draw on denominational/theological statements to advocate for easing or even erasing digital divides?"
This bears breaking down a bit further for clarification. What is a digital divide? A digital divide is best defined by Susan Crawford as she talks about her book Captive Audience, which refers to the chasm that exists between those who can afford to purchase access to the internet and the devices needed to access it, and those who cannot. Crawford remarks that this is an issue of justice, because so much of our economy revolves around being connected via the web. Job applications, applications for benefits, etc, require one be connected. And this is not just about getting onto social networks, online shopping, and catching up on cat videos. This is the very engine that powers our economy and is the thing on which self-sufficiency is built.
To break this down even further, I would like to share some of my personal experiences from my past work in human services. In order to get food stamps or other benefits, you can only apply online. Okay. You do not have a computer at home. You go to the library. In order to use public computers you must have a library card, which probably requires that you prove your address with a utilities bill or get a statement from your case manager that states that you are homeless. If you don't have an ID card, you won't necessarily be able to get a library card either. At any rate, you won't be able to get onto the computer that day. If you manage to get that information you go back to the library and find that you can sign up for a one hour time slot. But there are several people ahead of you and the wait is three hours. In your one hour time slot you start an application, but since you don't know much about computers, it is pretty difficult to accomplish anything. You leave vowing to come back the next day. Except you don't have any bus fare. Or childcare. In order to get assistance with your utilities and stay in your home, you have to call at exactly the right time, which is 9:00am. Except you have an appointment at the food bank this morning which you have waited for two weeks to receive and can't stay near your home phone (which is funded by a grant from your city as an emergency-only service). You don't have a cell phone because you cannot afford one. So you have to make the difficult decision of feeding your family right now or getting help with your gas bill. These are just two examples of things I encountered over and over again.
Your sense of digital divide is further exacerbated when you try and apply for jobs or even if you are offered a job, you must have computer skills. Maybe you have been incarcerated and have very few computer skills. Maybe you are a senior citizen with little reason or desire to use computers, but now that you are facing unemployment and debt in what should be your retirement years, you have to learn in order to continue working. Maybe English is not your first language. Maybe mental illness, post-traumatic stress, or other health concerns cause you anxiety about being online. Even if you have a laptop, computer skills, and the desire to get online, most places that advertise "free wi-fi" are coffee shops and you must actually purchase something while you are there. So if you cannot afford your own access at home, you still have to pay for it somewhere. I agree with Crawford, access to the internet is not a luxury. It is a necessity and it is an issue of social justice.
There are many excellent non-profit organizations providing computer access and computer skills classes, I used to work for one, Denver Urban Ministries, teaching computer classes and job skills. I do not think it is the responsibility of faith communities to duplicate services already being offered elsewhere. I do think the answer for communities of faith is to direct their resources (financial and volunteer) towards organizations who are already doing excellent work.
But I think it is the responsibility of communities of faith to look at their stated convictions and act accordingly with their time, talents, and treasure. At the very minimum, this means setting aside the free-market mentality that dominates our culture and realizing our responsibilities to one another in the interconnected body of Christ.
In my research, I discovered two social statements from the ELCA that could be applicable here. Both are a little dated, particularly with as quickly as our wired world progresses. The statement on Economic Life: Sufficient and Sustainable Livelihood for All (1999) recognizes that increased prosperity for some has the flip side of increased misery for more vulnerable people. It also acknowledges that not all benefit from capitalism, and boldly states, "we affirm that God promises a world where there is enough for everyone, if we would only learn how to use and share what God has given for the sake of all."
The other social statement from the ELCA that applies is the statement on Education (2007) which advocates for equal and quality access to education for all people as it relates to the command to serve out one's vocation. To the glory of God we are to fulfill our role in the priesthood of all believers, and education allows for this to be actualized. This statement makes a commitment to ensuring high-quality education for all children as a justice issue.
All that is to say that the problem of digital divide is systematic and complex. And I am not at all convinced that churches are poised to take the lead in lessening or erasing it when we are still having hotheaded debates about whether or not the church newsletter should be electronic and if churches should have an account on Facebook and if the pastor has a twitter account. The ELCA has already made some powerful statements about social justice, but I fear that we are too entrenched in our own fears about technology to effect any real change on a level of justice.