What is Reddit's opinion of Contact Backup?

From 3.5 billion Reddit comments

It is strange behaviour indeed. If you can backup contacts to computer that would be safe first, or you could try using an app from the play store.

And then try clearing app data

I can think of few ways. If you have adb working (you should be able to enable it and allow debugging without function keys), you may try using input events to "click" menu button: http://stackoverflow.com/questions/7789826/adb-shell-input-events . There are also pre-made tools to control your device with broken screen/touch as long as you have debugging working: http://forum.xda-developers.com/showthread.php?t=2786395 You may also try to install some extra software that allows you to export to .vcf without digging through menu, like this one: https://play.google.com/store/apps/details?id=com.tos.contact (looks free and seems to allow to export .vcf directly).
You may also work with 3rd party tools like mobiledit to dump data on PC.