No, the law is quite clear employers can not legally infringe or discriminate, and one of the protected areas is political expression.
Employers can suppress political expression in the work place to a degree, but not out of the workplace.
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The National Labor Relations Act, which does cover private employers, may not apply directly to political speech per se in the private workplace. However, it does give non-supervisory employees a limited right to engage in free speech and other protected concerted activities for their “mutual aid and protection.”
For example, under this federal labor law, employees may wear union buttons or insignia in the workplace, absent special circumstances. They may engage in solicitations for political causes on their employer’s property so long as neither the employee doing the solicitation and the employee being solicited are not engaging in such activities during working time.
Similarly, employees may engage in distribution of political materials on the employer’s property so long as the distribution does not occur in working areas. Moreover, employers who allow candidates to come on to their property and campaign, may undermine their rights to maintain and enforce otherwise lawful limits on employee solicitation or distribution.
Court rulings and opinions of the General Counsel of the National Labor Relations Board (NLRB) also make it clear that employees can engage in political campaign activities that may be contrary to the interests or positions of their employer. For example, discharging employees for campaigning against immigration reform or for repeal of a state’s right to work law would be unlawful.
The NLRB has also recently been very active in applying the right of employees to engage in protected concerted activities for their mutual aid and protection to social media such as Facebook and Twitter — even when the employees are not working. The NLRB has published three extensive reports in the past year expounding on these rights. Thus, employers should be careful to appreciate and not violate rights of employees who exercise their emerging rights to use such forms of social media.
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https://www.tlnt.com/political-speech-in-the-workplace-employers-beware/