Why he was pushed out was never confirmed. For "being a Trump supporter" makes for a nice counter-culture story, but doesn't make much sense given how openly Peter Theil campaigned for Trump.
I think he was fired because he was generating a lot of negative press/attention for what was at that time a burgeoning VR project dependent on adoption by a crowd that largely wasn't a fan of his political leanings...basically office politics.
But...he was fired with a $100 million severance [2], so it's not much of a pity situation.
1 - https://www.theatlantic.com/technology/archive/2016/09/reven...
2- https://www.fastcompany.com/90266150/zuck-pressured-facebook...