Please notice that you changed my example to something else.
Yes I did. If Peterson is correct a hotel will be unable to fire a male receptionist who turns up in a dress and a beard claiming that this is his/her/they/Zi version of "gender expression". That would be a bad law.
You believe that it should be legal to fire a fireman for coming out trans?
No.
For instance, suppose a female fireman comes out as a man, you believe it should be possible to fire that person?
No absolutely not. Not unless something interferes with their ability to perform their duties.
Again if Peterson is correct, the fireman/woman will be able to demand that they are referred to by made-up pronouns. They employer would be liable for the failure of other employees to comply. IF Peterson's interpretation is correct.