If you're a grammar purist, you might argue that you should only use due to after a verb like is, but most people accept that using it after other verbs is okay.
Normal Person:
Jeff Probst thinks that people get voted off the island because of their inability to play a good social game.
OR
Jeff Probst thinks that people get voted off the island due to their inability to play a good social game.
Grammar Purist:
Jeff Probst thinks that people get voted off the island because of their inability to play a good social game.