Answer:
This one is complicated. If you have a social media policy for your Staff Handbook you should enforce it accordingly. If not, we definitely recommend creating a social media policy to include in your Staff Handbook. The policy should prohibit this type of behavior and will give you a clear and concrete standard to which you can hold employees accountable.
In the present situation, you are caught between policies and laws that prohibit discrimination and harassment and laws that protect an employee’s speech (NLRA and Title VII religious protections).
If the employee made no threats, statements about co-workers, and isn't a supervisor, it may be best to let it go until you have a social media policy in place.
If you do address it, we suggest a meeting with the employee (and a third party witness) to explain the reaction and ask them to make the page (or post) private. Make it clear this is voluntary, you’re not disciplining them or discouraging free expression, but are concerned these views may be misinterpreted as the organization's views based on their identification as your employee.
If the employee’s post is harassing, identifying, or disparaging co-workers or constituents or if the language itself is hate-speech, you have more cause to intervene with disciplinary action. If you do decide to take disciplinary action or terminate, we recommend you involve legal counsel.