Not even sure if they would classify themselves as Christians, but what is their view on social media?
Unfortunately, the Amish are a hard group to get a grasp on.
First you have to clarify which order of Amish. There are some super conservative groups which are more like what most people have been taught to envision when they think of Amish.
The majority of your basic "Old Order" Amish have electricity, just not on the grid, through generators, batteries and even solar. It's not present inside the home, but is often in their barns and offices. They do have phones, usually the land-line is in a phone booth outside (notice the emphasis on the home). They mostly have cell phones, at least for business, but they are cracking down on smart phones with internet.
Internet is the real key. It's access to dangerous things (primarily pornography is pointed at) makes it the real problem with computers. Not the computer itself. Amish use "word processors" ever day at our work. They are PCs made with modified network cards so they are incapable of connecting to the internet with a browser.
Bishops are figuring out that smart phones are basically just small computers with internet, so that is being discouraged. (My Amish boss had an iPhone for business for several years up until 6 months ago, now he's back to basic flip phone, as are the others in his Bishop's district).
Obviously, no internet means no social media. However the kids have smart phones and facebook and all that and there doesn't seem to be any issue with it. Though it is family by family what the kids are allowed to do. The children aren't bound by Amish rules since they aren't a part of the church until they choose, so it's up to the parents.
Judging by its use by the teenagers, the Amish parents have no moral issue with social media. It's use by full members of the church would clearly not be allowed as it requires the use of the internet. But any Amish rule against something cannot be equated as an absolute moral judgment against it.
They wouldn't look down on you for your facebook, at least not any more than they would for you watching TV or driving them to the store in your car.
Most information I have given is from personal daily contact with the Amish in Pennsylvania. However this article highlights some of the things I reference: http://www.buzzfeed.com/justinesharrock/the-surprising-ingenious-amish-gadget-culture#.wnob1lVjG