Regardless of whether or not it's Constitutional, I believe we need to expand first amendment rights with regard to what people say outside of working hours.
So long as a person doesn't claim to be speaking as a representative of his company, and so long as the speech is protected (i.e. does not incite violence, etc.) then an individual should not have to worry about losing his/her job because of statements made outside work.
We are entering a time where companies are making claims over the entire lives of their employees. They are requiring their employees to behave in certain ways and abstain from certain activities supposedly because of health concerns. They are scouring employees' social media to see if those employees share the same worldview and the company purports to hold in their mission statements.
This frankly is Orwellian even if it is not being done by the government.
Saying that employees can go get a job elsewhere or go work for themselves if they want to speak their minds is no answer. The leftists that gained control of the academies and media decades ago now have control over the corporate boards and offices. There will soon be no place for conservatives to work if we dare speak our minds outside of work.
More gubmint is not the answer, and while we're at it, let's shred the Constitution.