When I opened android studio today, it showed me the following errors:

TL;DR
I finally fixed it by removing .idea/workspace.xml and reenabling plugins worked.
Same issue happened to me when I installed AS 3.1 beta alongside AS 3.0.1(stable) and opened my project in it. It was ok for few sessions, until it wasn't. Can't figure out what exactly broke project configuration, but project would open in 3.0.1 and not in 3.1. Any other project would work on 3.1 too. Symptoms were the same: android support plugin is disabled, and it wouldn't enable. I tried invalidating caches, reinstalling AS (even 3.1 stable version won't work).
Eventually I noticed projectBackup and projectBackup2 folders created by studio in the project's root folder. They contained versions of workspace.xml file. So I removed these backup folders, and workspace.xml from .idea folder. Then studio asked to reload project and that's it - after that I could reenable all the plugins