I think you're way into the weeds here and forget the most important thing to remember about "freedom": things like the Bill of Rights and the Constitution are a compact between you and the government, not you and private companies. Private companies don't owe you anything besides whatever the government has expressly legislated, such as explicit protection for religious clothing and icons like crosses, Sikh turbans, etc.
However, beyond that, individual companies have the right to request their employees look and dress in certain ways. The flip side there is, if you don't like those rules, you are free to not work there anymore.
Of course, legislators can always choose to pass laws forcing companies to allow more exemptions, but that hasn't happened yet for displays of a political organisation.