I don't think free speech is an "anytime, anyplace" thing. I've heard people assert that free speech means you have a "right to be heard" which to me is nonsense. People can talk all they want, but nobody has to listen. Your free speech has to be compelling enough to get people to listen.
Also, if you're being paid to do work, shut up and work! Unless you can walk and chew bubble gum at the same time, but even then- don't distract the people you work with.
Venue matters too. Follow the house rules, and use common sense. There's some really stupid people thinking they are doing "free speech" - if you're just shouting at someone to drown out what they are saying that's you trying to censor them, not exercising free speech.
So, ultimately it depends on what you mean- because sometimes when people are "silenced" it's because they were trying to abuse free speech. As somebody who voted for President Trump- I don't care that youtube/facebook/twitter kicked him off because it's their platforms. I'm also irritated that he said he was creating a competing platform and then never did. I don't agree with white supremacy but the Charlottesville protest thing was their right- and from what I understand they had a permit to do it while the counterprotesters didn't. If your "counterprotest" doesn't get a permit when a permit is required- that's not free speech, that's just you trying to violate someone else's free speech that you don't like.
So there are some circumstances when people being "silenced" isn't a really a violation of their free speech, because they really weren't exercising free speech to begin with. But yeah, if someone is exercising free speech in good faith, they shouldn't be silenced. Except for Marxists, they should always be silenced (just kidding. Without Marxists, who would we pour out all our severe criticisms and harsh rebukes?).