In general, freedom of speech is one of the places where conservatives tend to do a lot better than liberals. You are making a really good example of that.
Freedom of speech has nothing to do with private parties exacting revenge on you for saying, doing, or promoting objective wrongness.
Freedom of speech is not freedom of equality of validness of opinion.
"Freedom of speech" is a concept that is bigger and more far reaching than the government. If someone threatens to punch you in the face for saying something that he doesn't want you to say, he has violated your freedom of speech.
If your employer fires you for something that you said outside of work and separate from your duties as an employee, that employer has also violated your freedom of speech. The notable difference being that in most circumstances, there's nothing illegal about that.
The point that I'm making here is that it's absolutely possible to suppress suppress freedom of speech without violating the law.
In contrast being shouted down at a meeting or losing your job is common and not protected. If your employer doesn't want to support your opinions, they are free to stop paying you. That is a freedom too.
I think it is very important that bosses embrace this view too, because otherwise you just get a lot of sycophantic yes-men, an echo chamber. The correct approach is to let everyone be free to voice their opinion before the decision is made: if you don't want their opinions, then what are you paying them for? Once a decision is made it is necessary for everybody to work towards that, but making a good decision requires lots of input, and those who disagreed with the final choice shouldn't be punished in any way, otherwise there quickly won't be any disagreement.