Is there actually any US law against discrimination based on political stance?
TLDR: yes, and there are certain exceptions, IANAL so not sure where this particular case falls
"However, there are exceptions. For instance, if you participate in a political activity that creates a conflict of interest with your employer's business model, your job could potentially be on the line"
The whole thing here emphasis mine: No employer shall make, adopt, or enforce any rule, regulation, or policy:
(a) Forbidding or preventing employees from engaging or participating in politics or from becoming candidates for public office.
(b) Controlling or directing, or tending to control or direct the political activities or affiliations of employees.
It seems that Google has to have a specific policy in place for this law to be triggered, which does not seem to be the claim being made.
No. It would be enough for there to be a demonstrated consistent set of actions in a specific direction. Otherwise, many other laws could be made moot by companies not having a specific written policy, but still carrying out such actions.
It's not super clear to me that this would protect Damore, but IANAL.
PS. Being told that "You are only here because you're a diversity hire, you can't actually do the work," is creating a hostile working environment.