In the context of work "silencing" could mean preventing workers from raising (valuable) concerns about the ethics of their work.
And again, the only people I've seen making this argument have ethics and hold values that are in line with the company's values. I've never seen a liberal at a conservative company call for more political discussion, or vice versa. It's always been conservatives in conservative companies or liberal in liberal companies making this argument. People who hold views contrary to the company mostly stay quiet, because making their views known results in ostracism and other negative consequences.
I think the primary motivation is that people whose views are in line with the company enjoy the situation of voicing their positions while being immune to challenge because people who disagree with them are pressured into silence. It produces a gratifying sense for the people in th majority, but comes at the expense of people in the minority. For that reason, there's good cause to not allow political discussion in the workplace.
It's better to just not let anyone use the company as a soapbox at all. If they have disagreements about the culture of the company, there are plenty of reporters looking for a scoop.
In my experience, most people who complain that curbing political discussion in the workplace amounts to silencing them have views that are well in line with the status quo at the company.