Certainly in the US if you are an at-will private employee you can be terminated for any reason or no reason at all, except for explicitly protected classes. Political affiliation is not a protected class, at least not on a Federal level, although a few states have varying degrees of protection [0] that may have protected this staffer. As for government employees, the situation is more complicated. If you are a low-level government employee, your political affiliation is not valid grounds for being terminated. However, employees who are considered as placed in "policymaking" [1] roles, which would include being an "adviser" [1] of some sort, would be able to be terminated according to US standards.

[0] https://www.shrm.org/resourcesandtools/legal-and-compliance/...

[1] Elrod v. Burns, 427 U.S. 347 (1976). Also see Rutan v. Republican Party of Illinois, 497 U.S. 62 (1990).