The key word in the question is "discussed". Provided there is no interference with the purpose of the employment, healthy discussions regarding any topic work to provide more information to people and expand their knowledge of the topic at hand. Limiting any controversial topic from discussion would be unhealthy and an inappropriate move on the part of any company.
Politics is a subject that should be discussed openly in the public sphere so that information, ideas and opinions can be expressed and spread. There actually can be a spirit of a healthy exchange of ideas which can be fun and not intimidating withing the workplace. A workplace that discourages freedom of thought and speech is not a very healthy organization.
No, politics should not be discussed at work. Most people take their political views very, very seriously and discussions can become quite heated and passionate. Politics should be discussed someplace where there are no time constraints, where you are not on a company time clock. There’s always that chance that a political discussion at work could easily get out of control and end up costing someone their job.
It depends on the type of work naturally, but in general it is a good idea to avoid discussing controversial topics such as politics at work as it can distract from or disrupt the working environment. Politics often cause serious disagreements and animosity between people. This could naturally become a problem for people who must work with each other every day.