On a rooted Android device, TitaniumBackup can be used this way (not factory updates, but those don't get wiped by factory reset anyway).
However, it doesn't solve your real problem, which is that you can be compelled to log into your social media accounts in the presence of the border control officers. You can do that from the browser on a wiped phone, or on their equipment.
Yeah, it's true. I guess it would be one part of a strategy. Mine also involves saying "pardon me?" a lot and telling them that I'm deaf. 98% of people in uniform don't have the patience to try to communicate with a deaf person, and just tell me to move along. Also, they probably won't believe that I don't have facebook or email, but I can avoid telling them about things like okcupid, instagram, and disqus logins at least long enough to delete those accounts if I do get searched. Like any security, it's more of a deterrence than an absolute block.
However, it doesn't solve your real problem, which is that you can be compelled to log into your social media accounts in the presence of the border control officers. You can do that from the browser on a wiped phone, or on their equipment.