At will employment is not so simple. As an employer, I know that if I fire someone, & give no reason, I'm somewhat protected.
But if I give a reason which appears wrongful, I could suffer in court. Tis best to keep one's eyes open, & one's mouth shut.
To fire a deputy for liking the sheriff's opponent looks odious to me.
Yes, you do have to tread lightly in dismissing someone. There cannot be a hint of discrimination. I had to jump through hoops to fire a woman who did nothing but challenge me as her manager. She was completely insubordinate. I had to devise one aptitude test for my entire staff. It was an extremely simple test that everyone passed except her. That, her excessive absences and her insubordination were my grounds for her dismissal. And even then it had to be adjudicated by my v.p.
But consider that the deputy sheriff is a public servant under one administration who is openly endorsing an opponent of the administration he represents. Even if he has legal recourse, it's highly unprofessional and unethical.