If their job requires them to operate autonomously from authority and engage in critical thinking, going to a "stop the steal" protest would seem to be strong indicators against those skills in both regards.
Also
If the employee's actions being there (regardless of "where exactly" the employee was) is causing a huge distraction (problems) to running of the business, then the employee should be let-go.
If you look at the percentages of people who believe in moronic conspiracy theories about the moon landing, the Holocaust and so on, you’ll find this principle unsustainable. There are a lot of people who are capable of doing decent jobs while failing to engage their brains in politics - in fact, the vast majority of people do this, albeit to a lesser extent than Qanoners in most cases.
Agreed.
I found your examples amusing as I once had a colleague who was convinced the moon landing was faked along with a host of other conspiracy theories, yet was also one of the more competent Chartered Accountants in the office. Turns out his ridiculous opinions didn't inhibit his critical thinking skills or ability to work autonomously in accountancy. Surprising I know.
Similarly Ben Carson believed all sorts of weird stuff, but that didn't prevent him from doing all those brain surgeries successfully.
The notion that being laughably wrong in one area renders one unfit to work in a thinking profession is one of the more bizarre takes that crops up on Atlas from time to time. I think it betrays a certain lack of real world experience. People are weird and complicated, and often don't fit to our little psephological boxes. I think we're all better off for it.