Then this applies to being a racist, sexist, bigot, etc. You cut out being a Nazi, but that would apply here. And people get fired for being a Nazi all the time and no one gets upset. You want to make the argument of what a basic freedom is, but then want exceptions. Those exception fundamentally change the rule. "Freedoms "in a free society are checked all the time. You can't discriminate in your hiring practices based on race or sex anymore. You can't enter into a slavery agreement even if both sides are "willing".
You mention avoiding persecution. Its the same for those that own companies. People who own companies, run them, are also allowed freedom in such a society. Fundamental freedoms have to do with government. Trying to keep them from placing restriction on private citizens.
And lets be clear, we have protection for workers. You can't get fired for being a practicing Christian, Muslim, etc. You can't be fired for being a Democrat or Republican. But claiming religious or political affiliation does make you immune to your action. You can't cloak your racism, your sexism, in the idea that it is your religious or political right, is BS. And you can get fired for acting like bigot, even when invoking your religion or political party.