Here's the thing, you either support freedom of speech and expression, or you don't. Now if you do, then you have to support the nazi's right to speak and express, the abortion doctor's right to speak and express, the senator's right to speak and express, and the beggar's right to speak and express.
Everyone's right must be supported. If someone wants to express themselves to my boss via boycott in an effort to get me fired, so be it. That's their right. Just as it's the nazi's right to express himself on the internet to better inform people about the tenets of his ideology. The government must have no ability to constrict either activity.
It may not seem like it, but it's actually a good thing that the government can't stop any of these people from doing any of these things.
If you want to get the government to disallow any boycotts of companies, then you are not really in favor of freedom of speech and expression.