Yes, it is possible to get fired for being rude to your boss in front of another employee or in any other context. Workplace behavior, including how employees communicate with their superiors, is subject to certain standards and expectations. Being rude, disrespectful, or insubordinate to a boss can be considered misconduct, and many companies have policies in place that address such behavior.
The severity of the consequences will depend on various factors, such as the company's culture, the extent of the rudeness, the frequency of such behavior, and whether there have been any prior incidents. In some cases, a first offense may result in a warning or disciplinary action, but repeated instances or particularly egregious behavior could lead to termination of employment.
It's essential for employees to maintain a level of professionalism and respect in their interactions with supervisors and colleagues to foster a healthy work environment. If there are concerns or issues with a boss, it is generally better to address them through proper channels, such as discussing them privately or bringing them up with HR, rather than resorting to rude behavior.