I had this problem on my Asus TF300T tablet running Android 4.2.1. After clearing the data, removing all updates for the Netflix app and updating again, the issue was still there. It turns out that Netflix is very finicky about the network you're connected to. Mine has two routers: one for the wired devices and one for the wireless devices. The gateway is on the wired router and the wireless router goes out through it. Some posts advice to run a WAN test on the router and that's when I realized that the internal tools in the wireless router do not have access to the internet, although every wireless device connected to it has internet access, including my tablet in question. I switched the operation mode on the wireless router from router to access point. That fixed the Netflix sign in problem for me.
If you find that nothing works for you at home, try connecting somewhere else. If you have specific DNS servers in your (Android) network setup try without them.