You cannot prevent your employees from discussing wages. It is literally illegal to do so, and you cannot reprimand people for doing so.

Under the National Labor Relations Act (NLRA or the Act), employees have the right to communicate with their coworkers about their wages, as well as with labor organizations, worker centers, the media, and the public. Wages are a vital term and condition of employment, and discussions of wages are often preliminary to organizing or other actions for mutual aid or protection.

If you are an employee covered by the Act, you may discuss wages in face-to-face conversations, over the phone, and in written messages. Policies that specifically prohibit the discussion of wages are unlawful as are policies that chill employees from discussing their wages.

You may have discussions about wages when not at work, when you are on break, and even during work if employees are permitted to have other non-work conversations. You have these rights whether or not you are represented by a union.

https://www.nlrb.gov/about-nlrb/rights-we-protect/your-rights/your-rights-to-discuss-wages

It's not illegal. It's frown upon both socially and at the work culture. It makes people uncomfortable.

Doesn't mean you shouldn't. Ripping farts is frowned upon/makes people uncomfortable too.