Q: Can my company treat employees adversely because of their personal political beliefs? If they wear a shirt of their favorite candidate? Or proselytize about their candidate?
A: The short answer: There exists no “First Amendment Right to freedom of expression” in a private workplace, and that extends to political expression. See Manhattan Community Access Corp. v. Halleck, 139 S.Ct. 1921 (2019) (Only “State actors subject to First Amendment constraints.”)
So, yes, legally a private employer can refuse to hire Democrats or Republicans, and can fire an employee for wearing a shirt of their candidate or vocalizing a particular political position.
On the other hand, other laws can apply, such as the right to “concerted action” under the National Labor Relations Act. Overt adverse action also could be ripe for allegations of selective enforcement, such as “you only selectively enforce this rule against me because I am ___________”, where Title VII covers race, sex, religion, color and national origin; ADA covers disability; ADEA age, etc. Some political positions could easily bleed over into religious beliefs.
Even if legally permissible for a private employer to discriminate against holders of one particular political belief, from a practical management perspective, it cannot be recommended, and would be loaded with risk. Also, it could simply make for bad optics and make it harder to attract and retain the best talent.
Finally, this answer changes entirely for public employers and government employers, where employees do possess First Amendment rights, so long as, in general, they are speaking (1) as a private citizen, (2) about a matter of public concern, and (3) their speech does not interfere with the job. There are exceptions for high-ranking individuals, political appointees or someone trying to release classified information, though in many instances they would still be protected from retaliation.