This is exactly what happened in the NBA when a similar misfit went through the same charade back in the 1990s.
“Employers have wide discretion when it comes to limiting the political expression of employees in the workplace. The First Amendment generally applies only to government censorship of speech. As such, the Constitution allows private companies to regulate speech, even to bar political discussion entirely...
...In general, regardless of a particular state’s rules regarding political expression in the workplace, an employer can discipline or discharge an employee for legitimate, business-related reasons, even if the conduct involves political expression at work. For example, if an employee’s political expression interferes with his/her work, disrupts his/her co-workers, or infringes upon a business objective, the employer can take action consistent with its written policies and practices.”