I can't tell you to go somewhere else in a public space. Neither of us own the place.
Why should I go somewhere else, when you're the one who should be getting vaccinated? If you're not vaccinated, then maybe you should just stay at home so you don't spread your pathogens.
The government can't force you against your will, but the government also has the responsibility of protecting other citizens. Not "forcing" is not an absolute value, just like freedom of speech isn't an absolute value. Some expressions are not protected under freedom of speech.
It is about harassment, under this law. Even if you have no intention of harassing someone, it could count as harassment.
The real issue is why should all the other groups and attributes such as gender, race, age, etc., be protected under this law, but not "gender identity"? That is indeed singling out and discriminating gender identity.
Well you're changing the subject, because nobody is getting fired over this. At best you're getting fined, or forced to apologize, or take some courses in human rights. Of course if you refuse to do that, then it turns into a criminal case of not paying fines, which is a separate issue.