Public vs private is irrelevant. There are just bigots who can not tolerate different opinions.
Nor are they obligated to. To paraphrase, I may defend your right to speak your opinion but I am not required to be your friend or to spare you from any social consequences of your speech. Make no mistake, there has never been a time when unpopular speech did not have consequences for the speaker and if this bothers you then feel free to exercise your right not to speak or select a society that shares your beliefs.
Freedom of speech means the government cannot throw you in jail for the things you say. That is it. Short of violence, everyone else has the freedom of speech to tell you how reprehensible you are without limitations.
This idea that people have the right to say whatever they want without repercussions due to "freedom of speech" is a meme that needs to go away.
Quoting from http://volokh.com/2013/08/06/lawsuit-over-firing-based-on-em...
In 1937, “the California Legislature, recognizing that employers could misuse their economic power to interfere with the political activities of their employees, enacted Labor Code sections 1101 and 1102 to protect the employees’ rights.” Labor Code section 1101 provides: “No employer shall make, adopt, or enforce any rule, regulation, or policy: [¶] (a) Forbidding or preventing employees from engaging or participating in politics …. [or] (b) Controlling or directing, or tending to control or direct the political activities or affiliations of employees.” Labor Code section 1102 provides: “No employer shall coerce or influence or attempt to coerce or influence his employees through or by means of threat of discharge or loss of employment to adopt or follow or refrain from adopting or following any particular course or line of political action or political activity.” These sections are designed to protect “ ‘the fundamental right of employees in general to engage in political activity without interference by employers.’ ”
Now it can be used to protect those who political beliefs are more on the right. How the worm turns!