Can I tell employee to please shut up? Well, it depends
Sometimes the schoolteacher refrains "everyone be quiet" or "back to your corners" can feel like an excellent tool for managing employees. Be aware of the pitfalls, however, when you ask them to avoid certain topics of conversation or behave in a particular way.
Nonwork-related chatter or just being a jerk
As employers, we already ask people to avoid certain kinds of language or conversations at work. For example, we don't allow employees to discuss their sexual activities, use racial epithets, or make discriminatory statements about people and their physical or mental abilities.
When something doesn't clearly fall within the Equal Employment Opportunity Commission's (EEOC) guidelines, however, it can be a bit more difficult to determine what an employee may or may not talk about in the workplace. That has been particularly true during intense political seasons when conversations about both local and national races can step well over the line of basic politeness.
In general, if employees engage in disruptive debates about something innocuous like their preferred TV programs or opinions on the designated hitter rule in major league baseball, you can ask them to cease the conversations. While it's difficult to police personal discussions, you have the right to ask people to stop arguing about certain topics.