No, you can't fire someone for their views. That's 100% illegal, but given the track record of our current Supreme Court, I don't see that being the case for long.
Yes, in general a private employer can legally fire an employee for their political views. There are exceptions in some states, including California, New York, Colorado, North Dakota, that have protections for firing by political affiliation or activities, but that's the exception to the rule. Another exception applies to any public employee, since the first amendment applies to their employer.
The default employment rule is at-will, meaning someone can be fired for any reason not explicitly prohibited. Political affiliation is not a federally protected category.
> The default employment rule is at-will employment, meaning someone can be fired for any reason not explicitly prohibited.
Even then, in practice they can fire people for prohibited reasons, as long as it can't be proven that those reasons were used. Which in practice could be very difficult.
The default employment rule is at-will, meaning someone can be fired for any reason not explicitly prohibited. Political affiliation is not a federally protected category.