I don't think you can categorically place Musk into any political ideology. To be honest I see him like I saw myself as a teenager, whiffling in between different beliefs constantly.
That's fine, but the reality is that this article is grasping for outage from progressive ideologues and there's clearly no evidence to support the notion that he's 'cleaning house'. Firing two people with a self-appointed title out of a 10% layoff amounts to happenstance