Yes. Person with Tourette should not be fired for saying things that others don't.
(discussing norms, not free speech as legal rights below)
The norms in private organizations (companies, universities, associations) are different for different people.
1) If you are representative of an organization, what you say in private reflects your organization and it's reputation. It's established norm that personal values and opinions publicly expressed can't deviate from that of the organization. This includes many low level customer service jobs.
2) Low level managers, teachers and coaches are in position of authority and their whole identity is involved. Leader can shout their mouth about their political opinions and people working under them are not in position to talk back. That's not proper position to be politically opinionated. There are some norms limiting to their self expression in private, but it's usually context dependent.
3) Low level workers without public position or responsibilities over other should get most leeway to be whatever they are outside the job. When I was working in the floor level warehouse, the coffee break was the most politically diverse environment. Anarchist and far-right guy sitting next to each other debating angrily about women's rights, unions, Jews, holocaust. Nobody considered taking it upstairs because it was offensive. Only cases of bullying were considered out of line.