Yes, an employer can fire his employee for attending a protest. If an employee participates in a rally of protest outside of working hours, a private employer who finds the same can subsequently fire him. The laws of a democratic country protect an employees’ right to attend protests that are lawful, but no law can protect him or her from the employment consequences. However, from state to state the laws differ. Some state laws are a little liberal while some are not. Hence, talking in general, an employer can fire his employee for attending a protest rally outside of working hours. 

The different States Hold Different Laws For The Same

• Laws in California: As per the laws here, an employer cannot fire his employee from job for participating in a rally or protest, if the protest is a lawful protest and does not include any damage to the state or its people. Also if an employer demotes, suspends, or discharges any of his employees for lawful conduct during nonworking hours, which was conducted away from his premises, will have to compensate for the loss of wages to the said employee. 
• Laws in Colorado: In Colorado also the laws are pretty much the same as in California. Here also an employer cannot fire his employee for attending a lawful protest. However, if an employer terminates the employment of his employee on the grounds that he or she was engaged in any lawful activity away from the employer’s premises during nonworking hours then he (employer) is considered to have discriminated and shall have to face the repercussions.
• Louisiana: The law of Louisiana prohibits any employer from terminating an employee if he or she was engaged or was participating in politics. The laws further prohibit him from coercing or influencing any of the employees by means of threats such as discharging or firing from employment if the said employee gets affiliated to or participate in political activities. 
• New York: The law in New York is no different than the laws mentioned in the above three states. However, the New York law prohibits any kind of discrimination done by the employer for any leisure-time activity, or a lawful activity done by employee for which the employee receives no compensation. In simple terms, if an employee spends some of his time in recreational activities which are lawful, and for which the employee does not receive any compensation from the employer then the employer cannot discriminate, or fire the employee on the said grounds.

Based on the laws mentioned by each state it is evident that if an employee gets involved in any unlawful activity or any unlawful protest which the laws condemn the employers can fire their employees for the same. 

Conclusion

In a nutshell, there is no federal legislation, which can protect employees from getting fired for attending a protest. Hence it’s obligatory for employees to pay close attention to his or her employer’s policies before getting involved in such activities.