Damore's memo was titled "Google's Ideological Echo Chamber". It definitely gets discussed as anti-conservatism in conservative circles. The only places that attack it as "Damore thinks women are worse than men" are the sort of liberal outlets that Republicans don't read much.
If you're like most people on HN you probably don't consume much conservative media. Or at least way less than the President does. If you're curious as to what sort of thing his circle are reading, go look here:
https://www.breitbart.com/tech/
Note the nature of the stories. Many of them are about tech firms apparently discriminating against or attacking conservatives and conservative politicians. Also note that people don't really distinguish between tech firms. Twitter, Facebook, Google, Amazon. They're all seen as basically the same group of people and in fairness, they kinda are ... Facebook was built in the early days by poaching lots of Googlers.
By the way, anyone who reads across the spectrum will quickly notice that Google News seems to have silently blacklisted Breitbart. It's indexed, but never ranks and doesn't auto-complete. Instead the ranking reliably pushes liberal outlets to the fore. I read across the spectrum - NYT, Guardian, Telegraph, Breitbart, Washington Post, whatever gets linked here. Google News very obviously wants me to read certain worldviews much more than others. The UI doesn't make that obvious though.
Google's institutional hatred of the Republican party is by now old news. I'll be really upset if this leads to a win for Oracle. APIs should not be copyrightable but it's not obvious why not to people who aren't developers.